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Gauge theories with matter fields in various representations play an important role in different branches of physics. Recently, it was proposed that several aspects of the interesting pseudogap phase of cuprate superconductors near optimal doping may be explained by an emergent $SU(2)$ gauge symmetry. Around the transition with positive hole-doping, one can construct a $(2+1)-$dimensional $SU(2)$ gauge theory coupled to four adjoint scalar fields which gives rise to a rich phase diagram with a myriad of phases having different broken symmetries. We study the phase diagram of this model on the Euclidean lattice using the Hybrid Monte Carlo algorithm. We find the existence of multiple broken phases as predicted by previous mean field studies. Depending on the quartic couplings, the $SU(2)$ gauge symmetry is broken down either to $U(1)$ or $\mathbb{Z}_2$ in the perturbative description of the model. We further study the confinement-deconfinement transition in this theory, and find that both the broken phases are deconfining in the range of volumes that we studied. However, there exists a marked difference in the behavior of the Polyakov loop between the two phases., Comment: 11 pages, 11 figures, minor changes to results and conclusions

Using tensor network methods, we simulate the real-time evolution of the lattice Thirring model quenched out of equilibrium in both the critical and massive phases, and study the appearance of dynamical quantum phase transitions, as non-analyticities in the Loschmidt rate. Whereas the presence of a dynamical quantum phase transition in the model does not correspond to quenches across the critical line of the equilibrium phase diagram at zero temperature, we identify a threshold in the energy density of the initial state, necessary for a dynamical quantum phase transition to be present. Moreover, in the case of the gapped quench Hamiltonian, we unveil a connection of this threshold to a transition between different regions in the finite temperature phase diagram.

Electronic liquid crystal (ELC) phases are spontaneous symmetry breaking states believed to arise from strong electron correlation in quantum materials such as cuprates and iron pnictides. Here, we report a direct observation of ELC phases in a Dirac nodal line (DNL) semimetal GdSbxTe2-x. Electronic nanostructures consisting of incommensurate smectic charge modulation and intense local nematic order are visualized by using spectroscopic imaging - scanning tunneling microscopy. As topological materials with symmetry protected Dirac or Weyl fermions are mostly weakly correlated, the discovery of such ELC phases are anomalous and raise questions on the origin of their emergence. Specifically, we demonstrate how chemical substitution generates these symmetry breaking phases before the system undergoes a charge density wave - orthorhombic structural transition. We further show how dopants can induce nematicity via quasiparticle scattering interference. Our results highlight the importance of impurities in realizing ELC phases and present a new material platform for exploring the interplay among quenched disorder, topology and electron correlation.

We introduce a tensor network library designed for classical and quantum physics simulations called Cytnx (pronounced as sci-tens). This library provides almost an identical interface and syntax for both C++ and Python, allowing users to effortlessly switch between two languages. Aiming at a quick learning process for new users of tensor network algorithms, the interfaces resemble the popular Python scientific libraries like NumPy, Scipy, and PyTorch. Not only multiple global Abelian symmetries can be easily defined and implemented, Cytnx also provides a new tool called Network that allows users to store large tensor networks and perform tensor network contractions in an optimal order automatically. With the integration of cuQuantum, tensor calculations can also be executed efficiently on GPUs. We present benchmark results for tensor operations on both devices, CPU and GPU. We also discuss features and higher-level interfaces to be added in the future.

We study a 3-dimensional SU(2) gauge theory with 4 Higgs fields which transform under the adjoint representation of the gauge group, that has been recently proposed by Sachdev et al. to explain the physics of cuprate superconductors near optimal doping. The symmetric confining phase of the theory corresponds to the usual Fermi-liquid phase while the broken (Higgs) phase is associated with the interesting pseudogap phase of cuprates. We employ the Hybrid Monte-Carlo algorithm to study the phase diagram of the theory. We find the existence of a variety of broken phases in qualitative accordance with earlier mean-field predictions and discuss their role in cuprates. In addition, we investigate the behavior of Polyakov loop to probe the confinement/deconfinement phase transition, and find that the Higgs phase hosts a stable deconfining phase consistent with previous studies., Comment: 7 pages, 4 figures, Proceedings of the 40th International Symposium on Lattice Field Theory (LATTICE2023), July 31st - August 4th, 2023, Fermi National Accelerator Laboratory

We study the most general Two Higgs Doublet Model with $SU(2)$ gauge fields on the lattice. The phase space is probed through the computation of gauge-invariant global observables serving as proxies for order parameters. In each phase, the spectrum of the theory is analysed for different combinations of bare couplings and different symmetry breaking patterns. The scale setting and determination of the running gauge coupling are performed through the Wilson flow computation of the action density.

Topology plays a crucial role in many physical systems, leading to interesting states at the surface. The paradigmatic example is the Chern number defined in the Brillouin zone that leads to the robust gapless edge states. Here we introduce the reduced Chern number, defined in subregions of the Brillouin zone (BZ), and construct a family of Chern dartboard insulators (CDIs) with quantized reduced Chern numbers in the sub-BZ (sBZ) but with trivial bulk topology. CDIs are protected by mirror symmetries and exhibit distinct pseudospin textures, including (anti)skyrmions, inside the sBZ. These CDIs host exotic gapless edge states, such as M\"{o}bius fermions and midgap corner states, and can be realized in photonic crystals. Our work opens up new possibilities for exploring sBZ topology and nontrivial surface responses in topological systems.

We propose a scheme to perform tensor network based finite-size scaling analysis for two-dimensional classical models. In the tensor network representation of the partition function, we use higher-order tensor renormalization group (HOTRG) method to coarse grain the weight tensor. The renormalized tensor is then used to construct the approximated transfer matrix of an infinite strip of finite width. By diagonalizing the transfer matrix we obtain the correlation length, the magnetization, and the energy density which are used in finite-size scaling analysis to determine the critical temperature and the critical exponents. As a benchmark we study the two-dimensional classical Ising model. We show that the critical temperature and the critical exponents can be accurately determined. With HOTRG bond dimension $D=70$, the absolute errors of the critical temperature $T_c$ and the critical exponent $\nu$, $\beta$ are at the order of $10^{-7}, 10^{-5}$, $10^{-4}$ respectively. Furthermore, the results can be systematically improved by increasing the bond dimension of the HOTRG method. Finally, we study the length scale induced by the finite cut-off in bond dimension and elucidate its physical meaning in this context.

We study two different SU(2) gauge-scalar theories in 3 and 4 spacetime dimensions. Firstly, we focus on the 3 dimensional SU(2) theory with multiple Higgs fields in the adjoint representation, that can be mapped to cuprate systems in condensed matter physics which host a rich phase diagram including high-Tc superconductivity. It has been proposed that the theory with 4 adjoint Higgs fields can be used to explain the physics of hole-doped cuprates for a wide range of parameters. We show exploratory results on the phase diagram of the theory. On the other hand, we are interested in the 4 dimensional theory with 2 sets of fundamental scalar (Higgs) fields, which is relevant to the 2 Higgs Doublet Model (2HDM), a proposed extension to the Standard Model of particle physics. The goal is to understand the particle spectrum of the theory at zero temperature and the electroweak phase transition at finite temperature. We present exploratory results on scale setting and the multi-parameter phase diagram of this theory., Comment: 10 pages, 5 figures, Proceedings of the 39th International Symposium on Lattice Field Theory (LATTICE2022), 8th-13th August 2022, Bonn, Germany

We propose a simple and generic construction of the variational tensor network operators to study the quantum spin systems by the synergy of ideas from the imaginary-time evolution and variational optimization of trial wave functions. By applying these operators to simple initial states, accurate variational ground state wave functions with extremely few parameters can be obtained. Furthermore, the framework can be applied to study spontaneously symmetry breaking, symmetry protected topological, and intrinsic topologically ordered phases, and we show that symmetries of the local tensors associated with these phases can emerge directly after the optimization without any gauge fixing. This provides a universal way to identify quantum phase transitions without prior knowledge of the system., Comment: 16 pages, 12 figures

Bulk-boundary correspondence serves as an important feature of the strong topological insulators, including Chern insulators and $Z_2$ topological insulators. Under nontrivial band topology, the protected gapless edge states correspond to the Wannier obstruction or Wilson-loop winding in the bulk. Recent studies show that the bulk topological features may not imply the existence of protected gapless edge states. Here we address the opposite question: Does the existence of protected gapless edge states necessarily imply the Wannier obstruction or Wilson-loop winding? We provide an example where the protected gapless edge states arise without the aforementioned bulk topological features. This trivialized topological insulator belongs to a new class of systems with non-delta-like Wannier functions. Interestingly, the gapless edge states are not protected by the crystalline symmetry; instead the protection originates from the mirror antisymmetry, a combination of chiral and mirror symmetries. Although the protected gapless edge states cannot be captured by the bulk topological features, they can be characterized by the spectral flow in the entanglement spectrum., Comment: 7 pages, 4 figures

Recent advance in classical reinforcement learning (RL) and quantum computation (QC) points to a promising direction of performing RL on a quantum computer. However, potential applications in quantum RL are limited by the number of qubits available in the modern quantum devices. Here we present two frameworks of deep quantum RL tasks using a gradient-free evolution optimization: First, we apply the amplitude encoding scheme to the Cart-Pole problem; Second, we propose a hybrid framework where the quantum RL agents are equipped with hybrid tensor network-variational quantum circuit (TN-VQC) architecture to handle inputs with dimensions exceeding the number of qubits. This allows us to perform quantum RL on the MiniGrid environment with 147-dimensional inputs. We demonstrate the quantum advantage of parameter saving using the amplitude encoding. The hybrid TN-VQC architecture provides a natural way to perform efficient compression of the input dimension, enabling further quantum RL applications on noisy intermediate-scale quantum devices.

We numerically study the phase structure of the CP(1) model in the presence of a topological $\theta$-term, a regime afflicted by the sign problem for conventional lattice Monte Carlo simulations. Using a bond-weighted tensor renormalization group method, we compute the free energy for inverse couplings ranging from $0\leq \beta \leq 1.1$ and find a CP-violating, first-order phase transition at $\theta=\pi$. In contrast to previous findings, our numerical results provide no evidence for a critical coupling $\beta_c<1.1$ above which a second-order phase transition emerges at $\theta=\pi$ and/or the first-order transition line bifurcates at $\theta\neq\pi$. If such a critical coupling exists, as suggested by Haldane's conjecture, our study indicates that is larger than $\beta_c>1.1$., Comment: 10 pages, 9 figures, v2: updated to match journal version

We generalize a tensor-network algorithm to study thermodynamic properties of self-similar spin lattices constructed on a square-lattice frame with two types of couplings, $J_{1}^{}$ and $J_{2}^{}$, chosen to transform a regular square lattice ($J_{1}^{} = J_{2}^{}$) onto a fractal lattice if decreasing $J_{2}^{}$ to zero (the fractal fully reconstructs when $J_{2}^{} = 0$). We modified the Higher-Order Tensor Renormalization Group (HOTRG) algorithm for this purpose. Single-site measurements are performed by means of so-called impurity tensors. So far, only a single local tensor and uniform extension-contraction relations have been considered in HOTRG. We introduce ten independent local tensors, each being extended and contracted by fifteen different recursion relations. We applied the Ising model to the $J_{1}^{}-J_{2}^{}$ planar fractal whose Hausdorff dimension at $J_{2}^{} = 0$ is $d^{(H)} = \ln 12 / \ln 4 \approx 1.792$. The generalized tensor-network algorithm is applicable to a wide range of fractal patterns and is suitable for models without translational invariance.

We study the excitation spectrum of the spin-1 Kitaev model using the symmetric tensor network. By evaluating the virtual order parameters defined on the virtual Hilbert space in the tensor network formalism, we confirm the ground state is in a $\mathbb{Z}_2$ spin liquid phase. Using the correspondence between the transfer matrix spectrum and low-lying excitations, we find that contrary to the dispersive Majorana excitation in the spin-1/2 case, the isotropic spin-1 Kitaev model has a dispersive charge anyon excitation. Bottom of the gapped single-particle charge excitations are found at $\mathbf{K}, \mathbf{K}'=(\pm2\pi/3, \mp 2\pi/3)$, with a corresponding correlation length of $\xi \approx 6.7$ unit cells. The lower edge of the two-particle continuum, which is closely related to the dynamical structure factor measured in inelastic neutron scattering experiments, is obtained by extracting the excitations in the vacuum superselection sector in the anyon theory language, Comment: 7 pages, 8 figures

We develop two novel numerical schemes to study the conductance of the two-wire junction of inequivalent Tomonaga-Luttinger Liquids. In the first scheme we use the static current-current correlation function across the junction to extract the linear conductance through a relation that is derived via the bosonization method. In the second scheme we apply a bias and evaluate the time-dependent current across the junction to obtain the current-voltage characteristic. The conductance is then extracted from the small bias result within the linear response regime. Both schemes are based on the infinite size matrix product state to minimize the finite-size effects. Due to the lack of the translational invariance, we focus on a finite-size window containing the junction. For time-independent calculations, we use infinite boundary conditions to evaluate the correlations within the window. For time-dependent calculations, we use the window technique to evaluate the local currents within the window. The numerical results obtained by both schemes show excellent agreement with the analytical predictions., Comment: 11 pages, 10 figures

We propose a unified scheme to identify phase transitions out of the $\mathbb{Z}_2$ Abelian topological order, including the transition to a non-Abelian chiral spin liquid. Using loop gas and and string gas states [H.-Y. Lee, R. Kaneko, T. Okubo, N. Kawashima, Phys. Rev. Lett. 123, 087203 (2019)] on the star lattice Kitaev model as an example, we compute the overlap of minimally entangled states through transfer matrices. We demonstrate that, similar to the anyon condensation, continuous deformation of a $\mathbb{Z}_2$-injective projected entangled-pair state (PEPS) also allows us to study the transition between Abelian and non-Abelian topological orders. We show that the charge and flux anyons defined in the Abelian phase transmute into the $\sigma$ anyon in the non-Abelian topological order. Furthermore, we show that contrary to the claim in [Phys. Rev. B 101, 035140 (2020)], both the LG and SG states have infinite correlation length in the non-Abelian regime, consistent with the no-go theorem that a chiral PEPS has a gapless parent Hamiltonian., Comment: 9 pages, 9 figures, published version

We introduce a hybrid model combining a quantum-inspired tensor network and a variational quantum circuit to perform supervised learning tasks. This architecture allows for the classical and quantum parts of the model to be trained simultaneously, providing an end-to-end training framework. We show that compared to the principal component analysis, a tensor network based on the matrix product state with low bond dimensions performs better as a feature extractor for the input data of the variational quantum circuit in the binary and ternary classification of MNIST and Fashion-MNIST datasets. The architecture is highly adaptable and the classical-quantum boundary can be adjusted according the availability of the quantum resource by exploiting the correspondence between tensor networks and quantum circuits., Comment: 13 pages, 5 figures. arXiv admin note: text overlap with arXiv:2011.14651

One key step in performing quantum machine learning (QML) on noisy intermediate-scale quantum (NISQ) devices is the dimension reduction of the input data prior to their encoding. Traditional principle component analysis (PCA) and neural networks have been used to perform this task; however, the classical and quantum layers are usually trained separately. A framework that allows for a better integration of the two key components is thus highly desirable. Here we introduce a hybrid model combining the quantum-inspired tensor networks (TN) and the variational quantum circuits (VQC) to perform supervised learning tasks, which allows for an end-to-end training. We show that a matrix product state based TN with low bond dimensions performs better than PCA as a feature extractor to compress data for the input of VQCs in the binary classification of MNIST dataset. The architecture is highly adaptable and can easily incorporate extra quantum resource when available., Comment: 8 pages, 7 figures, and 1 table. Proceeding for the First Workshop on Quantum Tensor Networks in Machine Learning, 34th Conference on Neural Information Processing Systems (NeurIPS 2020), Vancouver, Canada

The key idea behind the renormalization group (RG) transformation is that properties of physical systems with very different microscopic makeups can be characterized by a few universal parameters. However, finding the optimal RG transformation remains difficult due to the many possible choices of the weight factors in the RG procedure. Here we show, by identifying the conditional distribution in the restricted Boltzmann machine (RBM) and the weight factor distribution in the RG procedure, an optimal real-space RG transformation can be learned without prior knowledge of the physical system. This neural Monte Carlo RG algorithm allows for direct computation of the RG flow and critical exponents. This scheme naturally generates a transformation that maximizes the real-space mutual information between the coarse-grained region and the environment. Our results establish a solid connection between the RG transformation in physics and the deep architecture in machine learning, paving the way to further interdisciplinary research., Comment: 11 pages, 7 figures

We introduce a general method for optimizing real-space renormalization-group transformations to study the critical properties of a classical system. The scheme is based on minimizing the Kullback-Leibler divergence between the distribution of the system and the normalized normalizing factor of the transformation parametrized by a restricted Boltzmann machine. We compute the thermal critical exponent of the two-dimensional Ising model using the trained optimal projector and obtain a very accurate thermal critical exponent $y_t=1.0001(11)$ after the first step of the transformation., Comment: Published as a proceeding of Workshop on Machine Learning and the Physical Sciences at the 33rd Conference on Neural Information Processing Systems (NeurIPS) https://ml4physicalsciences.github.io/

We present concluding results from our study for zero-temperature phase structure of the massive Thirring model in 1+1 dimensions with staggered regularisation. Employing the method of matrix product states, several quantities, including two types of correlators, are investigated, leading to numerical evidence of a Berezinskii-Kosterlitz-Thouless phase transition. Exploratory results for real-time dynamics pertaining to this transition, obtained using the approaches of variational uniform matrix product state and time-dependent variational principle, are also discussed., Comment: 7 pages, 4 figures, contribution to the 37th International Symposium on Lattice Field Theory (LATTICE2019), 16-22 June 2019, Wuhan, China

Quantum entanglement is fragile to thermal fluctuations, which raises the question whether finite temperature phase transitions support long-range entanglement similar to their zero temperature counterparts. Here we use quantum Monte Carlo simulations to study the third Renyi negativity, a generalization of entanglement negativity, as a proxy of mixed-state entanglement in the 2D transverse field Ising model across its finite temperature phase transition. We find that the area-law coefficient of the Renyi negativity is singular across the transition, while its subleading constant is zero within the statistical error. This indicates that the entanglement is short-ranged at the critical point despite a divergent correlation length. Renyi negativity in several exactly solvable models also shows qualitative similarities to that in the 2D transverse field Ising model., Comment: 5 pages, 3 figures, 4 page appendix

We study the two-dimensional kagome-ice model derived from a pyrochlore lattice with second- and third-neighbor interactions. The canted moments align along the local $\langle 111 \rangle$ axes of the pyrochlore and respond to both in-plane and out-of-plane external fields. We find that the combination of further-neighbor interactions together with the external fields introduces a rich phase diagram with different spin textures. Close to the phase boundaries, metastable $\textit{"snake"}$ domains emerge with extremely long relaxation time. Our kinetic Monte Carlo analysis of the magnetic-field quench process from saturated state shows unusually slow dynamics. Despite that the interior spins are almost frozen in snake domains, the spins on the edge are free to fluctuate locally, leading to frequent creation and annihilation of monopole-anti-monopole bound states. Once the domains are formed, these excitations are localized and can hardly propagate due to the energy barrier of snakes. The emergence of such snake domains may shed light on the experimental observation of dipolar spin ice under tilted fields, and provide a new strategy to manipulate both spin and charge textures in artificial spin ice., Comment: 8 pages, 6 figures

Employing matrix product states as an ansatz, we study the non-thermal phase structure of the (1+1)-dimensional massive Thirring model in the sector of vanishing total fermion number with staggered regularization. In this paper, details of the implementation for this project are described. To depict the phase diagram of the model, we examine the entanglement entropy, the fermion bilinear condensate and two types of correlation functions. Our investigation shows the existence of two phases, with one of them being critical and the other gapped. An interesting feature of the phase structure is that the theory with non-zero fermion mass can be conformal. We also find clear numerical evidence that these phases are separated by a transition of the Berezinskii-Kosterlitz-Thouless type. Results presented in this paper establish the possibility of using the matrix product states for probing this type of phase transition in quantum field theories. They can provide information for further exploration of scaling behaviour, and serve as an important ingredient for controlling the continuum extrapolation of the model., Comment: 31 pages, 18 figures; minor changes to the text, typos corrected, references added; version published in Physical Review D

We present a deep reinforcement learning framework where a machine agent is trained to search for a policy to generate a ground state for the square ice model by exploring the physical environment. After training, the agent is capable of proposing a sequence of local moves to achieve the goal. Analysis of the trained policy and the state value function indicates that the ice rule and loop-closing condition are learned without prior knowledge. We test the trained policy as a sampler in the Markov chain Monte Carlo and benchmark against the baseline loop algorithm. This framework can be generalized to other models with topological constraints where generation of constraint-preserving states is difficult., Comment: 10 pages, 13 figures, 2 tables. Published version

We present a simple and efficient tensor network method to accurately locate phase boundaries of two-dimensional classical lattice models. The method utilizes only the information-theoretic (von Neumann) entropy of quantities that automatically arise along tensor renormalization group [Phys. Rev. Lett. \textbf{12}, 120601 (2007)] flows of partition functions. We benchmark the method against theoretically known results for the square-lattice $q$-state Potts models, which includes first-order, weakly first-order, and continuous phase transitions, and find good agreement in all cases. We also compare against previous Monte Carlo results for the frustrated square lattice $J_1-J_2$ Ising model and find good agreement., Comment: 9 pages, 4 figures, 2 tables. v2: updated figure for clarity and fixed reference typos. v3: improved data. v4: expanded intro., more data/figures. v5: added appendix

We present preliminary results of a study on the non-thermal phase structure of the (1+1) dimensional massive Thirring model, employing the method of matrix product states. Through investigating the entanglement entropy, the fermion correlators and the chiral condensate, it is found that this approach enables us to observe numerical evidence of a Kosterlitz-Thouless phase transition in the model., Comment: 7 pages, 4 figures; contribution to the proceedings of Lattice 2018 conference

A preponderance of evidence suggests that the ground state of the nearest-neighbor $S = 1/2$ antiferromagnetic Heisenberg model on the kagome lattice is a gapless spin liquid. Many candidate materials for the realization of this model possess in addition a Dzyaloshinskii-Moriya (DM) interaction. We study this system by tensor-network methods and deduce that a weak but finite DM interaction is required to destabilize the gapless spin-liquid state. The critical magnitude, $D_c/J \simeq 0.012(2)$, lies well below the DM strength proposed in the kagome material herbertsmithite, indicating a need to reassess the apparent spin-liquid behavior reported in this system., Comment: 9 pages, 9 figures, to appear in Phys. Rev. B

Quantum effect is expected to dictate the behaviour of physical systems at low temperature. For quantum magnets with geometrical frustration, quantum fluctuation usually lifts the macroscopic classical degeneracy, and exotic quantum states emerge. However, how different types of quantum processes entangle wave functions in a constrained Hilbert space is not well understood. Here, we study the topological entanglement entropy (TEE) and the thermal entropy of a quantum ice model on a geometrically frustrated kagome lattice. We find that the system does not show a $Z_2$ topological order down to extremely low temperature, yet continues to behave like a classical kagome ice with finite residual entropy. Our theoretical analysis indicates an intricate competition of off-diagonal and diagonal quantum processes leading to the quasi-degeneracy of states and effectively, the classical degeneracy is restored., Comment: 14 pages, 16 figures, added ED results for the effective model

An impurity in a Tomonaga-Luttinger liquid leads to a crossover between short- and long-distance regime which describes many physical phenomena. However, calculation of the entire crossover of correlation functions over different length scales has been difficult. We develop a powerful numerical method based on infinite DMRG utilizing a finite system with infinite boundary conditions, which can be applied to correlation functions near an impurity. For the $S=1/2$ chain, we demonstrate that the full crossover can be precisely obtained, and that their limiting behaviors show a good agreement with field-theory predictions.

Tensor Network methods have been established as a powerful technique for simulating low dimensional strongly-correlated systems for over two decades. Employing the formalism of Matrix Product States, we investigate the phase diagram of the massive Thirring model. We also show the possibility of studying soliton dynamics and topological phase transition via the Thirring model., Comment: 8 pages, 3 figures; contribution to the proceedings of the 35th International Symposium on Lattice Field Theory, 18 - 24 June 2017, Granada, Spain

The driven-dissipative Bose-Hubbard model can be experimentally realized with either negative or positive onsite detunings, inter-site hopping energies, and onsite interaction energies. Here we use one-dimensional matrix product density operators to perform a fully quantum investigation of the dependence of the non-equilibrium steady states of this model on the signs of these parameters. Due to a symmetry in the Lindblad master equation, we find that simultaneously changing the sign of the interaction energies, hopping energies, and chemical potentials leaves the local boson number distribution and inter-site number correlations invariant, and the steady-state complex conjugated. This shows that all driven-dissipative phenomena of interacting bosons described by the Lindblad master equation, such as "fermionization" and "superbunching", can equivalently occur with attractive or repulsive interactions., Comment: single column 12 pages, 4 figures, 1 table

We carry out simulated annealing and employ a generalized Kibble-Zurek scaling hypothesis to study the 2D Ising spin glass with normal-distributed couplings. The system has an equilibrium glass transition at temperature $T=0$. From a scaling analysis when $T\rightarrow 0$ at different annealing velocities, we extract the dynamic critical exponent $z$, i.e., the exponent relating the relaxation time $\tau$ to the system length $L$; $\tau\sim L^z$. We find $z=13.6 \pm 0.4$ for both the Edwards-Anderson spin-glass order parameter and the excess energy. This is different from a previous study of the system with bimodal couplings [S. J. Rubin, N. Xu, and A. W. Sandvik, Phys. Rev. E {\bf 95}, 052133 (2017)] where the dynamics is faster and the above two quantities relax with different exponents (and that of the energy is larger). We here argue that the different behaviors arise as a consequence of the different low-energy landscapes---for normal-distributed couplings the ground state is unique (up to a spin reflection) while the system with bimodal couplings is massively degenerate. Our results reinforce the conclusion of anomalous entropy-driven relaxation behavior in the bimodal Ising glass. In the case of a continuous coupling distribution, our results presented here indicate that, although Kibble-Zurek scaling holds, the perturbative behavior normally applying in the slow limit breaks down, likely due to quasi-degenerate states, and the scaling function takes a different form., Comment: 10 pages, 5 figures

The antiferromagnetic Ising chain in both transverse and longitudinal magnetic fields is one of the paradigmatic models of a quantum phase transition. The antiferromagnetic system exhibits a zero-temperature critical line separating an antiferromagnetic phase and a paramagnetic phase; the critical line connects an integrable quantum critical point at zero longitudinal field and a classical first-order transition point at zero transverse field. Using a strong-disorder renormalization group method formulated as a tree tensor network, we study the zero-temperature phase of the quantum Ising chain with bond randomness. We introduce a new matrix product operator representation of high-order moments, which provides an efficient and accurate tool for determining quantum phase transitions via the Binder cumulant of the order parameter. Our results demonstrate an infinite-randomness quantum critical point in zero longitudinal field accompanied by pronounced quantum Griffiths singularities, arising from rare ordered regions with anomalously slow fluctuations inside the paramagnetic phase. The strong Griffiths effects are signaled by a large dynamical exponent $z>1$, which characterizes a power-law density of low-energy states of the localized rare regions and becomes infinite at the quantum critical point. Upon application of a longitudinal field, the quantum phase transition between the paramagnetic phase and the antiferromagnetic phase is completely destroyed. Furthermore, quantum Griffiths effects are suppressed, showing $z<1$, when the dynamics of the rare regions is hampered by the longitudinal field., Comment: 13 pages, 10 figures

The spin-1 Haldane chain is an example of the symmetry-protected-topological (SPT) phase in one dimension. Experimental realization of the spin chain materials usually involves both the uniaxial-type, $D(S^z)^2$, and the rhombic-type, $E[(S^x)^2-(S^y)^2]$, single-ion anisotropies. Here, we provide a precise ground-state phase diagram for spin-1 Haldane chain with these single-ion anisotropies. Using quantum numbers, we find that the $\mathbb{Z}_2$ symmetry breaking phase can be characterized by double degeneracy in the entanglement spectrum. Topological quantum phase transitions take place on particular paths in the phase diagram, from the Haldane phase to the Large-$E_x$, Large-$E_y$, or Large-$D$ phases. The topological critical points are determined by the level spectroscopy method with a newly developed parity technique in the density matrix renormalization group [Phys. Rev. B 86, 024403 (2012)], and the Haldane-Large-$D$ critical point is obtained with an unprecedentedly precision, $(D/J)_c=0.9684713(1)$. Close to this critical point, a small rhombic single-ion anisotropy $|E|/J\ll1$ can destroy the Haldane phase and bring the system into a $y$-N\'eel phase. We propose that the compound [Ni(HF$_2$)(3-Clpy)$_4$]BF$_4$ is a candidate system to search for the $y$-N\'eel phase., Comment: Supplemental Material is included

Directly in the thermodynamic limit, we show how to combine imaginary and real time evolution of tensor networks to efficiently and accurately find the nonequilibrium steady states (NESS) of one-dimensional dissipative quantum lattices governed by the Lindblad master equation. The imaginary time evolution first bypasses any highly correlated portions of the real-time evolution trajectory by directly converging to the weakly correlated subspace of the NESS, after which real time evolution completes the convergence to the NESS with high accuracy. We demonstrate the power of the method with the dissipative transverse field quantum Ising chain. We show that a crossover of an order parameter shown to be smooth in previous finite-size studies remains smooth in the thermodynamic limit., Comment: 5+3 pages, 5 figures, 2 tables

We present numerical studies of dipolar spin ice in the presence of a magnetic field slightly tilted away from the [111] axis. We find a first-order transition from a kagome ice to a $\mathbf{q}=$X state when the external field is tilted toward the $[11\bar{2}]$ direction. This is consistent with the anomalous critical scattering previously observed in the neutron scattering experiment on the spin ice material $\textrm{Ho}_{2}\textrm{Ti}_{2}\textrm{O}_{7}$ in a tilted field [Nat. Phys. 3, 566 (2007)]. We show that this ordering originates from the antiferromagnetic alignment of spin chains on the kagome planes. The residual entropy of the kagome ice is fully recovered. Our result captures the features observed in the experiments and points to the importance of the dipolar interaction in determining ordered states in the spin ice materials. We place our results in the context of recent susceptibility measurements on $\textrm{Dy}_{2}\textrm{Ti}_{2}\textrm{O}_{7}$, showing two features for a [111] field., Comment: 5+1 pages; 5+2 figures

Inverse melting refers to the rare thermodynamic phenomenon in which a solid melts into a liquid upon cooling, a transition that can occur only when the ordered (solid) phase has more entropy than the disordered (liquid) phase, and that has so far only been observed in a handful of systems. Here we report the first experimental observation for the inverse melting of an electronic liquid crystalline order in strontium-doped lanthanum nickelate, a compound isostructural with the superconducting cuprates, with a hole doping concentration of 1/3. Using x-ray scattering, we demonstrate that the isotropic charge modulation is driven to nematic order by fluctuating spins and shows an inverse melting transition. Using a phenomenological Landau theory, we show that this inverse melting transition is due to the interlayer coupling between the charge and spin orders. This discovery points to the importance of the interlayer correlations in the system, and provides a new perspective to study the intricate nature of the electronic liquid crystal phases in strongly correlated electronic systems, including possibly the Cu- and Fe-based high-Tc superconductors., Comment: 7 pages, 7 figures

We propose an efficient numerical method, which combines the advantages of recently developed tensor-network based methods and standard trial wave functions, to study the ground state properties of quantum many-body systems. In this approach, we apply a projector in the form of a tensor-product operator to an input wave function, such as a Jastrow-type or Hartree-Fock wave function, and optimize the tensor elements via variational Monte Carlo. The entanglement already contained in the input wave function can considerably reduce the bond dimensions compared to the regular tensor-product state representation. In particular, this allows us to also represent states that do not obey the area law of entanglement entropy. In addition, for fermionic systems, the fermion sign structure can be encoded in the input wave function. We show that the optimized states provide good approximations of the ground-state energy and correlation functions in the cases of two-dimensional bosonic and fermonic systems., Comment: 7 pages, 5 figures, published version

We study numerically the universal conductance of Luttinger liquids wire with a single impurity via the Muti-scale Entanglement Renormalization Ansatz (MERA). The scale invariant MERA provides an efficient way to extract scaling operators and scaling dimensions for both the bulk and the boundary conformal field theories. By utilizing the key relationship between the conductance tensor and ground-state correlation function, the universal conductance can be evaluated within the framework of the boundary MERA. We construct the boundary MERA to compute the correlation functions and scaling dimensions for the Kane-Fisher fixed points by modeling the single impurity as a junction (weak link) of two interacting wires. We show that the universal behavior of the junction can be easily identified within the MERA and argue that the boundary MERA framework has tremendous potential to classify the fixed points in general multi-wire junctions., Comment: 14 pages, 18 figures

By using a different quantum-to-classical mapping from the Trotter-Suzuki decomposition, we identify the entanglement structure of the maximal eigenvectors for the associated quantum transfer matrix. This observation provides a deeper insight into the problem of linear growth of the entanglement entropy in time evolution using conventional methods. Based on this observation, we propose a general method for arbitrary temperatures using the biorthonormal transfer-matrix renormalization group. Our method exhibits a competitive accuracy with a much cheaper computational cost in comparison with two recent proposed methods for long-time dynamics based on a folding algorithm [Phys. Rev. Lett. 102, 240603 (2009)] and a modified time-dependent density-matrix renormalization group [Phys. Rev. Lett. 108, 227206 (2012)].

We report here numerical results of the low-temperature behavior of a dipolar spin ice in a magnetic field along the [100] direction. Tuning the magnetic field, the system exhibit a half-magnetization plateau at low temperature. This half-polarized phase should correspond to a quantum solid phase in an effective 2D quantum boson model, and the transition from the Coulomb phase with a power-law correlation to this state can be regarded as a superfluid to a quantum solid transition. We discuss possible experimental signatures of this half-polarized state., Comment: 7 pages, 9 figures; Published version

Symmetry-protected topological (SPT) phases are short-range entangled quantum phases with symmetry, which have gapped excitations in the bulk and gapless modes at the edge. In this paper, we study the SPT phases in the spin-1 Heisenberg chain with a single-ion anisotropy D, which has a quantum phase transition between a Haldane phase and a large-D phase. Using symmetric multiscale entanglement renormalization ansatz (MERA) tensor networks, we study the nonlocal order parameters for time-reversal and inversion symmetry. For the inversion symmetric MERA, we propose a brick-and-rope representation that gives a geometrical interpretation of inversion symmetric tensors. Finally, we study the symmetric renormalization group (RG) flow of the inversion symmetric string-order parameter, and show that entanglement renormalization with symmetric tensors produces proper behavior of the RG fixed-points., Comment: 11 pages, 18 figures

We test an improved finite-size scaling method for reliably extracting the critical temperature $T_{\rm BKT}$ of a Berezinskii-Kosterlitz-Thouless (BKT) transition. Using known single-parameter logarithmic corrections to the spin stiffness $\rho_s$ at $T_{\rm BKT}$ in combination with the Kosterlitz-Nelson relation between the transition temperature and the stiffness, $\rho_s(T_{\rm BKT})=2T_{\rm BKT}/\pi$, we define a size dependent transition temperature $T_{\rm BKT}(L_1,L_2)$ based on a pair of system sizes $L_1,L_2$, e.g., $L_2=2L_1$. We use Monte Carlo data for the standard two-dimensional classical XY model to demonstrate that this quantity is well behaved and can be reliably extrapolated to the thermodynamic limit using the next expected logarithmic correction beyond the ones included in defining $T_{\rm BKT}(L_1,L_2)$. For the Monte Carlo calculations we use GPU (graphical processing unit) computing to obtain high-precision data for $L$ up to 512. We find that the sub-leading logarithmic corrections have significant effects on the extrapolation. Our result $T_{\rm BKT}=0.8935(1)$ is several error bars above the previously best estimates of the transition temperature; $T_{\rm BKT} \approx 0.8929$. If only the leading log-correction is used, the result is, however, consistent with the lower value, suggesting that previous works have underestimated $T_{\rm BKT}$ because of neglect of sub-leading logarithms. Our method is easy to implement in practice and should be applicable to generic BKT transitions., Comment: 17 pages, 10 figures. v2: higher-order log-corrections taken into account. New value for the transition temperature

We perform large-scale Monte Carlo simulations of the classical XY model on a three-dimensional $L\times L \times L$ cubic lattice using the graphics processing unit (GPU). By the combination of Metropolis single-spin flip, over-relaxation and parallel-tempering methods, we simulate systems up to L=160. Performing the finite-size scaling analysis, we obtain estimates of the critical exponents for the three-dimensional XY universality class: $\alpha=-0.01293(48)$ and $\nu=0.67098(16)$. Our estimate for the correlation-length exponent $\nu$, in contrast to previous theoretical estimates, agrees with the most recent experimental estimate $\nu_{\rm exp}=0.6709(1)$ at the superfluid transition of $^4$He in a microgravity environment., Comment: 5 pages, 5 figures

We apply the biorthonormal transfer-matrix renormalization group (BTMRG) [Phys. Rev. E 83, 036702 (2011)] to study low-temperature properties of quantum spin chains. Simulation on isotropic Heisenberg spin-1/2 chain demonstrates that the BTMRG outperforms the conventional transfer-matrix renormalization group (TMRG) by successfully accessing far lower temperature unreachable by conventional TMRG, while retaining the same level of accuracy. The power of the method is further illustrated by the calculation of the low-temperature specific heat for a frustrated spin chain., Comment: 5 pages, 4 figures