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We generalize a tensor-network algorithm to study the 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 10 independent local tensors, each being extended and contracted by 15 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)}=ln12/ln4≈1.792. The generalized tensor-network algorithm is applicable to a wide range of fractal patterns and is suitable for models without translational invariance.

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-range 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.

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.

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.

We carry out simulated annealing and employ a generalized Kibble-Zurek scaling hypothesis to study the two-dimensional Ising spin glass with normal-distributed couplings. The system has an equilibrium glass transition at temperature T=0. From a scaling analysis when T→0 at different annealing velocities v, we find power-law scaling in the system size for the velocity required in order to relax toward the ground state, v∼L^{-(z+1/ν)}, the Kibble-Zurek ansatz where z is the dynamic critical exponent and ν the previously known correlation-length exponent, ν≈3.6. We find z≈13.6 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 [Rubin et al., Phys. Rev. E 95, 052133 (2017)2470-004510.1103/PhysRevE.95.052133] where the dynamics is faster (z is smaller) and the above two quantities relax with different dynamic exponents (with that of the energy being larger). We 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 also indicate that, although Kibble-Zurek scaling holds, the perturbative behavior normally applying in the slow limit breaks down, likely due to quasidegenerate states, and the scaling function takes a different form.

Directly in the thermodynamic limit, we show how to combine local imaginary and real-time evolution of tensor networks to efficiently and accurately find the nonequilibrium steady states (NESSs) of one-dimensional dissipative quantum lattices governed by a local 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.

We study the interplay of superfluidity, glassy, and magnetic orders in the XXZ model with random Ising interactions on a three dimensional cubic lattice. In the classical limit, this model reduces to a ±J Edwards-Anderson Ising model with concentration p of ferromagnetic bonds, which hosts a glassy-ferromagnetic transition at a critical concentration p(c)(cl)~0.77. Our quantum Monte Carlo simulation results show that quantum fluctuations stabilize the coexistence of superfluidity and glassy order (superglass), and shift the (super)glassy-ferromagnetic transition to p(c)>p(c)(cl). In contrast, antiferromagnetic order coexists with superfluidity to form a supersolid, and the transition to the glassy phase occurs at a higher p.

In a class of frustrated magnets known as spin ice, magnetic monopoles emerge as classical defects and interact via the magnetic Coulomb law. With quantum-mechanical interactions, these magnetic charges are carried by fractionalized bosonic quasi-particles, spinons, which can undergo Bose-Einstein condensation through a first-order transition via the Higgs mechanism. Here, we report evidence of a Higgs transition from a magnetic Coulomb liquid to a ferromagnet in single-crystal Yb(2)Ti(2)O(7). Polarized neutron scattering experiments show that the diffuse [111]-rod scattering and pinch-point features, which develop on cooling are suddenly suppressed below T(C)~0.21 K, where magnetic Bragg peaks and a full depolarization of the neutron spins are observed with thermal hysteresis, indicating a first-order ferromagnetic transition. Our results are explained on the basis of a quantum spin-ice model, whose high-temperature phase is effectively described as a magnetic Coulomb liquid, whereas the ground state shows a nearly collinear ferromagnetism with gapped spin excitations.

We present a method for contracting a square-lattice tensor network in two dimensions based on auxiliary tensors accomplishing successive truncations (renormalization) of eight-index tensors for 2 × 2 plaquettes into four-index tensors. Since all approximations are done on the wave function (which also can be interpreted in terms of different kinds of tensor networks), the scheme is variational, and thus, the tensors can be optimized by minimizing the energy. Test results for the quantum phase transition of the transverse-field Ising model confirm that even the smallest possible tensors (two values for each tensor index at each renormalization level) produce much better results than the simple product (mean-field) state., (© 2011 American Physical Society)

Using the example of Zn-doped La2CuO4, we demonstrate that a spinless impurity doped into a nonfrustrated antiferromagnet can induce substantial frustrating interactions among the spins surrounding it. This result is the key to resolving discrepancies between experimental data and earlier theories. Analytic and quantum Monte Carlo studies of the impurity-induced frustration are in a close accord with each other and experiments. The proposed mechanism should be common to other correlated oxides.

We present an algorithmic framework for a variant of the quantum Monte Carlo operator-loop algorithm, where nonlocal cluster updates are constructed in a way that makes each individual loop smaller. The algorithm is designed to increase simulation efficiency in cases where conventional loops become very large, do not close altogether, or otherwise behave poorly. We demonstrate and characterize some aspects of the short loop on a square lattice spin-1/2 XXZ model where, remarkably, a significant increase in simulation efficiency is observed in some parameter regimes. The simplicity of the model provides a prototype for the use of short loops on more complicated quantum systems.

Building on our understanding of the superfluid density rho(s)(T), we show how the pseudogap enters the in-plane optical conductivity sigma(omega,T) for temperatures T