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Scaling laws for critical phenomena take pivotal status in almost all branches of physics. However, as scaling laws are commonly guaranteed by the renormalization group theory, systems that violate them have rarely been found. In this letter, we demonstrate that gravitational system can break scaling laws. We derive this result through investigating phase transition and critical phenomenon in a gravitational system with quantum anomaly. For the first time, we outline the key conditions to violate the scaling laws in generic gravitational system viewed from the equation of state $P=P(T,V)$. Our results indicate that quantum effects can magnify the distinctiveness of gravity, which may be significant to understand the microscopic structure of spacetime., Comment: 7 pages, 3 figures

Deconfined quantum critical points (DQCPs) are proposed as unconventional second-order phase transitions beyond the Landau-Ginzburg-Wilson paradigm. The nature and experimental realizations of DQCPs are crucial issues of importance. We illustrate the potential for DQCPs between the valence bond solid state and the antiferromagnetic phase to arise in optical lattices containing frustrated dipolar bosons subject to hard-core constraints. The emergence of DQCPs is comprehended through the fusion of two Berezinskii-Kosterlitz-Thouless (BKT) transitions. The DQCPs and the BKTs are confirmed by the finite-size scaling of ground-state fidelity susceptibilities. The numerical analysis reveals varying critical exponents of the correlation length in DQCPs and the logarithmic scaling in BKTs, respectively. This work offers a promising platform for realizing DQCPs and provides valuable insights into their nature within the framework of topological phase transitions., Comment: 9 pages, 8 figures

In this study, we explore the quantum critical phenomena in generalized Aubry-Andr\'{e} models, with a particular focus on the scaling behavior at various filling states. Our approach involves using quantum fidelity susceptibility to precisely identify the mobility edges in these systems. Through a finite-size scaling analysis of the fidelity susceptibility, we are able to determine both the correlation-length critical exponent and the dynamical critical exponent at the critical point of the generalized Aubry-Andr\'{e} model. Based on the Diophantine equation conjecture, we can determines the number of subsequences of the Fibonacci sequence and the corresponding scaling functions for a specific filling fraction, as well as the universality class. Our findings demonstrate the effectiveness of employing the generalized fidelity susceptibility for the analysis of unconventional quantum criticality and the associated universal information of quasiperiodic systems in cutting-edge quantum simulation experiments., Comment: 9 pages, 5 figures

We investigate topological gauge-theory terms and quantum criticality in a spin-1 Kitaev chain with general single-ion anisotropies (SIAs). The ground-state phase diagram, including the Kitaev spin liquid (KSL) and gapless dimer phases, is determined by the infinite time evolving block decimation (iTEBD) method. A quantum phase transition between the KSL and dimer phases occurs by varying uniaxial SIA, analogous to the confinement-deconfinement transition in the lattice Schwinger model with a topological $\theta$ angle of $\pi$. Introducing rhombic SIA shifts this angle from $\pi$, resulting in $y$- and $x$-ferroquadrupole phases. The transition between these phases can occur through a crossover in the KSL phase or a genuine phase transition along a deconfined line. We map the spin-1 Hamiltonian to an effective spin-1/2 PXP Hamiltonian, with uniaxial SIA corresponding to uniform detuning and rhombic SIA to staggered detuning. We explore the hierarchical fragmentation of the Hilbert space, revealing that quantum many-body scars (QMBSs) emerge under weak uniform detuning, while slow dynamics under large staggered detuning is accurately captured by a second-order effective Hamiltonian via the Schrieffer-Wolff transformation. Our work establishes a framework for simulating topological $\theta$ angles and ergodicity-breaking dynamics, bridging higher-spin generalizations of scarred models with lattice gauge theories, potentially realizable using state-of-the-art cold-atom quantum simulators., Comment: 12 pages, 8 figures

Achieving precise preparation of quantum many-body states is crucial for the practical implementation of quantum computation and quantum simulation. However, the inherent challenges posed by unavoidable excitations at critical points during quench processes necessitate careful design of control fields. In this work, we introduce a promising and versatile dynamic control neural network tailored to optimize control fields. We address the problem of suppressing defect density and enhancing cat-state fidelity during the passage across the critical point in the quantum Ising model. Our method facilitates seamless transitions between different objective functions by adjusting the {optimization strategy}. In comparison to gradient-based power-law quench methods, our approach demonstrates significant advantages for both small system sizes and long-term evolutions. We provide a detailed analysis of the specific forms of control fields and summarize common features for experimental implementation. Furthermore, numerical simulations demonstrate the robustness of our proposal against random noise and spin number fluctuations. The optimized defect density and cat-state fidelity exhibit a transition at a critical ratio of the quench duration to the system size, coinciding with the quantum speed limit for quantum evolution., Comment: 14 pages, 9 figures; Accepted in Phys. Rev. A

In this paper, we investigate the gauge dependence of various physical observables in the quantum Rabi model (QRM) under different potential fields, arising from the Hilbert-space truncation of the atomic degree of freedom. We discover that in both the square-well potential and oscillator potential,the optimal gauges for the ground-state energy of the QRM vary with respect to the cavity frequency, with the dipole gauge being optimal in the low-frequency limit and the Coulomb gauge in the high-frequency limit of the cavity frequency. Additionally, for higher energy levels, the optimal gauge asymptotically approaches the dipole gauge. However, for the dynamical quantity out-time-order correlator (OTOC), we find the necessity to introduce an optimal dynamical gauge. We determine the optimal dynamical gauge by minimizing the mean error between the two-level OTOC and the full Hamiltonian one. We expect that this study will contribute to a more profound understanding of the subtle relation between gauge choice and the dynamics of QED systems.

In this study, we explore an approach aimed at enhancing the transmission or reflection coefficients of absorbing materials through the utilization of joint measurements of entangled photon states. On the one hand, through the implementation of photon catalysis in the reflected channel, we can effectively modify the state of the transmission channel, leading to a notable improvement in the transmission ratio. Similarly, this approach holds potential for significantly amplifying the reflection ratio of absorbing materials, which is useful for detecting cooperative targets. On the other hand, employing statistical counting methods based on the technique of heralding on zero photons, we evaluate the influence of our reflection enhancement protocol for detecting noncooperative targets, which is validated through Monte Carlo simulations of a quantum radar setup affected by Gaussian white noise. Our results demonstrate a remarkable enhancement in the signal-to-noise ratio of imaging, albeit with an increase in mean-square error. These findings highlight the potential practical applications of our approach in the implementation of quantum radar., Comment: 11 pages, 10 figures

Quantum control plays an irreplaceable role in practical use of quantum computers. However, some challenges have to be overcome to find more suitable and diverse control parameters. We propose a promising and generalizable average-fidelity-based machine-learning-inspired method to optimize the control parameters, in which a neural network with periodic feature enhancement is used as an ansatz. In the implementation of a single-qubit gate by cat-state nonadiabatic geometric quantum computation via reverse engineering, compared with the control parameters in the simple form of a trigonometric function, our approach can yield significantly higher-fidelity ($>99.99\%$) phase gates, such as the $\pi / 8$ gate (T gate). Single-qubit gates are robust against systematic noise, additive white Gaussian noise and decoherence. We numerically demonstrate that the neural network possesses the ability to expand the model space. With the help of our optimization, we provide a feasible way to implement cascaded multi-qubit gates with high quality in a bosonic system. Therefore, the machine-learning-inspired method may be feasible in quantum optimal control of nonadiabatic geometric quantum computation., Comment: 12 pages, 8 figures

To establish a solid-state-based framework for the coexistence of quantum many-body scars and quantum criticality, we investigate the spin-1 Kitaev chain with uniaxial single-ion anisotropy (SIA). In the subspace with uniform $\mathbb{Z}_2$ gauge fields, this model can be exactly mapped to the spin-1/2 effective detuned PXP Hamiltonian, where the SIA plays a role of the static detuning term. The quench dynamics starting from the product states is symmetric between positive and negative values of the SIA, while a quantum phase transition from the Kitaev spin liquid to the dimer phase only occurs at the critical point with a negative $D_c$, implying the spontaneous breaking of the translational symmetry. We find that the coherent oscillations of quantum fidelity and certain local observables are sustained against small SIA perturbations in a quantum quench from special initial states. While the oscillation amplitudes of these observables decay with time as the SIA strength is increased, the system completely thermalizes upon approaching the critical point. In contrast, the initial polarized state, which shows an absence of revivals of quantum fidelity, will exhibit long revivals for $D

We show that phase transitions in the quantum $q$-state clock model for $q \leq 4$ can be characterized by an enhanced decay behavior of the Loschmidt echo via a small quench. The quantum criticality of the quantum $q$-state clock model is numerically investigated by the finite-size scaling of the first minimum of the Loschmidt echo and the short-time average of the rate function. The equilibrium correlation-length critical exponents are obtained from the scaling laws which are consistent with previous results. Furthermore, we study dynamical quantum phase transitions by analyzing the Loschmidt echo and the order parameter for any $q$ upon a big quench. For $q \leq 4$, we show that dynamical quantum phase transitions can be described by the Loschmidt echo and the zeros of the order parameter. In particular, we find the rate function increases logarithmically with $q$ at the first critical time. However, for $q > 4$, we find that the correspondence between the singularities of the Loschmidt echo and the zeros of the order parameter no longer exists. Instead, we find that the Loschmidt echo near its first minimum converges, while the order parameter at its first zero increases linearly with $q$., Comment: 13 pages, 5 figures

We have investigated scaling properties near the quantum critical point between the extended phase and the critical phase in the Aubry-Andr\'{e}-Harper model with p-wave pairing, which have rarely been exploited as most investigations focus on the localization transition from the critical phase to the localized phase. We find that the spectrum averaged entanglement entropy and the generalized fidelity susceptibility act as eminent universal order parameters of the corresponding critical point without gap closing. We introduce a Widom scaling ansatz for these criticality probes to develop a unified theory of critical exponents and scaling functions. We thus extract the correlation-length critical exponent $\nu$ and the dynamical exponent $z$ through the finite-size scaling given the system sizes increase in the Fibonacci sequence. The retrieved values of $\nu \simeq 1.000$ and $z \simeq 3.610$ indicate that the transition from the extended phase to the critical phase belongs to a different universality class from the localization transition. Our approach sets the stage for exploring the unconventional quantum criticality and the associated universal information of quasiperiodic systems in state-of-the-art quantum simulation experiments., Comment: 14 pages, 8 figures, accepted by Physical Review B

Motivated by recent work on the non-Hermitian skin effect in the bosonic Kitaev-Majorana model, we study the quantum criticality of interacting bosonic Kitaev-Hubbard models on a chain and a two-leg ladder. In the hard-core limit, we show exactly that the non-Hermitian skin effect disappears via a transformation from hard-core bosonic models to spin-1/2 models. We also show that hard-core bosons can engineer the Kitaev interaction, the Dzyaloshinskii-Moriya interaction and the compass interaction in the presence of the complex hopping and pairing terms. Importantly, quantum criticalities of the chain with a three-body constraint and unconstrained soft-core bosons are investigated by the density matrix renormalization group method. This work reveals the effect of many-body interactions on the non-Hermitian skin effect and highlights the power of bosons with pairing terms as a probe for the engineering of interesting models and quantum phase transitions., Comment: 9 pages, 6 figures

In this paper, we show that an effective spin Hamiltonian with various types of couplings can be engineered using quantum simulators in atomic-molecular-optical laboratories, dubbed the \emph{XY}-Gamma model. We analytically solve the one-dimensional short-range interacting case with the Jordan-Wigner transformation and establish the phase diagram. In the gapless phase, an incommensurate spiral order is manifested by the vector-chiral correlations. Between distinct gapped phases, a logarithmic scaling behavior of local measures, including spin correlations and the steered quantum coherence, is identified for the quantum critical points, yielding a compelling value of the correlation-length critical exponent. We derive explicit scaling forms of the excitation gap near the quantum critical points. The extracted critical exponents reveal the quantum phase transition on the boundary of Tomonaga-Luttinger liquid belongs to Lifshitz universality class.Our results may provide useful insights into the underlying mechanism in quantum criticality for state-of-the-art experiments of quantum simulation., Comment: 15 pages, 10 figures

We study quantum phase transitions in Heisenberg antiferromagnetic chains with a staggered power-law decaying long-range interactions. Employing the density-matrix renormalization group (DMRG) algorithm and the fidelity susceptibility as the criticality measure, we establish more accurate values of quantum critical points than the results obtained from the spin-wave approximation, quantum Monte Carlo and DMRG in literatures. The deviation is especially evident for strong long-range interactions. We extend isotropic long-range interactions to the anisotropic cases and find that kaleidoscope of quantum phases emerge from the interplay of anisotropy of the long-range exchange interaction and symmetry breaking. We demonstrate nonfrustrating long-range interactions induce the true long-range order in Heisenberg antiferromagnetic chains with a continuous symmetry breaking, lifting the restrictions imposed by the Mermin-Wagner theorem., Comment: 9 pages, 11 figures

To provide a physical example of quantum scars, we study the many-body scars in the spin-1 Kitaev chain where the so-called PXP Hamiltonian is exactly embedded in the spectra. Regarding the conserved quantities, the Hilbert space is fragmented into disconnected subspaces and we explore the associated constrained dynamics. The continuous revivals of the fidelity and the entanglement entropy when the initial state is prepared in $\vert\mathbb{Z}_k\rangle$ ($k=2,3$) state illustrate the essential physics of the PXP model. We study the quantum phase transitions in the one-dimensional spin-1 Kitaev-Heisenberg model using the density-matrix renormalization group and Lanczos exact diagonalization methods, and determine the phase diagram. We parametrize the two terms in the Hamiltonian by the angle $\phi$, where the Kitaev term is $K\equiv\sin(\phi)$ and competes with the Heisenberg $J\equiv\cos(\phi)$ term. One finds a rich ground state phase diagram as a function of the angle $\phi$. Depending on the ratio $K/J\equiv\tan(\phi)$, the system either breaks the symmetry to one of distinct symmetry broken phases, or preserves the symmetry in a quantum spin liquid phase with frustrated interactions. We find that the scarred state is stable for perturbations which obey $\mathbb{Z}_2$-symmetry, while it becomes unstable against Heisenberg-type perturbations.\\ \textit{Accepted for publication in Physical Review Research}, Comment: 12 pages, 10 figures

We investigate the quantum criticality and universality in Aubry-Andr\'{e}-Harper (AAH) model with $p$-wave superconducting pairing $\Delta$ in terms of the generalized fidelity susceptibility (GFS). We show that the higher-order GFS is more efficient in spotlighting the critical points than lower-order ones, and thus the enhanced sensitivity is propitious for extracting the associated universal information from the finite-size scaling in quasiperiodic systems. The GFS obeys power-law scaling for localization transitions and thus scaling properties of the GFS provide compelling values of critical exponents. Specifically, we demonstrate that the fixed modulation phase $\phi=\pi$ alleviates the odd-even effect of scaling functions across the Aubry-Andr\'{e} transition with $\Delta=0$, while the scaling functions for odd and even numbers of system sizes with a finite $\Delta$ cannot coincide irrespective of the value of $\phi$. A thorough numerical analysis with odd number of system sizes reveals the correlation-length exponent $\nu \simeq 1.000$ and the dynamical exponent $z$ $\simeq$ 1.388 for transitions from the critical phase to the localized phase,suggesting the unusual universality class of localization transitions in the AAH model with a finite $p$-wave superconducting pairing lies in a different universality class from the Aubry-Andr\'{e} transition. The results may be testified in near term state-of-the-art experimental settings., Comment: 12 pages, 7 figures, accepted by Physical Review A

We make a first principle study of gravitational pressure in cosmic thermodynamics. The pressure is directly derived from the unified first law, in fact the Einstein field equation in spherically symmetric spacetime. By using this pressure, we obtain the thermodynamics for the FRW universe, especially presenting the gravitational equation of state for the FRW spacetime itself, i.e. $P=P(R_A, T)$ for the first time. Furthermore, we study the Joule-Thomson expansion as an application of the thermodynamic equation of state to find the cooling-heating property of the FRW universe. We demonstrate that there is an inversion temperature for a FRW universe if its enthalpy ${\cal H}$ is negative. These investigations shed insights on the evolution of our universe in view of thermodynamics., Comment: Some new footnotes added, and version published in JHEP

When the Rashba and Dresslhaus spin-orbit coupling are both presented for a two-dimensional electron in a perpendicular magnetic field, a striking resemblance to anisotropic quantum Rabi model in quantum optics is found. We perform a generalized Rashba coupling approximation to obtain a solvable Hamiltonian by keeping the nearest-mixing terms of Laudau states, which is reformulated in the similar form to that with only Rashba coupling. Each Landau state becomes a new displaced-Fock state with a displacement shift instead of the original Harmonic oscillator Fock state, yielding eigenstates in closed form. Analytical energies are consistent with numerical ones in a wide range of coupling strength even for a strong Zeeman splitting. In the presence of an electric field, the spin conductance and the charge conductance obtained analytically are in good agreements with the numerical results. As the component of the Dresselhaus coupling increases, we find that the spin Hall conductance exhibits a pronounced resonant peak at a larger value of the inverse of the magnetic field. Meanwhile, the charge conductance exhibits a series of plateaus as well as a jump at the resonant magnetic field. Our method provides an easy-to-implement analytical treatment to two-dimensional electron gas systems with both types of spin-orbit couplings., Comment: 9 pages,3 figures