We analytically and numerically study the Loschmidt echo and the dynamical order parameters in a spin chain with a deconfined phase transition between a dimerized state and a ferromagnetic phase. For quenches from a dimerized state to a ferromagnetic
phase, we find that the model can exhibit a dynamical quantum phase transition characterized by an associating dimerized order parameters. In particular, when quenching the system from the Majumdar-Ghosh state to the ferromagnetic Ising state, we find an exact mapping into the classical Ising chain for a quench from the paramagnetic phase to the classical Ising phase by analytically calculating the Loschmidt echo and the dynamical order parameters. By contrast, for quenches from a ferromagnetic state to a dimerized state, the system relaxes very fast so that the dynamical quantum transition may only exist in a short time scale. We reveal that the dynamical quantum phase transition can occur in systems with two broken symmetry phases and the quench dynamics may be independent on equilibrium phase transitions.
The out-of-time-ordered correlators (OTOC) have been established as a fundamental concept for quantifying quantum information scrambling and diagnosing quantum chaotic behavior. Recently, it was theoretically proposed that the OTOC can be used as an
order parameter to dynamically detect both equilibrium quantum phase transitions (EQPTs) and dynamical quantum phase transitions (DQPTs) in one-dimensional many-body systems. Here we report the first experimental observation of EQPTs and DQPTs in a quantum spin chain via quench dynamics of OTOC on a nuclear magnetic resonance quantum simulator. We observe that the quench dynamics of both the order parameter and the two-body correlation function cannot detect the DQPTs, but the OTOC can unambiguously detect the DQPTs. Moreover, we demonstrate that the long-time average value of the OTOC in quantum quench signals the equilibrium quantum critical point and ordered quantum phases, thus one can measure the EQPTs from the non-equilibrium quantum quench dynamics. Our experiment paves a way for experimentally investigating DQPTs through OTOCs and for studying the EQPTs through the non-equilibrium quantum quench dynamics with quantum simulators.
Degeneracy (exceptional) points embedded in energy band are distinct by their topological features. We report different hybrid two-state coalescences (EP2s) formed through merging two EP2s with opposite chiralities that created from the type III Dira
c points emerging from a flat band. The band touching hybrid EP2, which is isolated, is induced by the destructive interference at the proper match between non-Hermiticity and synthetic magnetic flux. The degeneracy points and different types of exceptional points are distinguishable by their topological features of global geometric phase associated with the scaling exponent of phase rigidity. Our findings not only pave the way of merging EPs but also shed light on the future investigations of non-Hermitian topological phases.
Deconfined quantum critical point was proposed as a second-order quantum phase transition between two broken symmetry phases beyond the Landau-Ginzburg-Wilson paradigm. However, numerical studies cannot completely rule out a weakly first-order transi
tion because of strong violations of finite-size scaling. We demonstrate that the fidelity is a simple probe to study deconfined quantum critical point. We study the ground-state fidelity susceptibility close to the deconfined quantum critical point in a spin chain using the large-scale finite-size density matrix renormalization group method. We find that the finite-size scaling of the fidelity susceptibility obeys the conventional scaling behavior for continuous phase transitions, supporting the deconfined quantum phase transition is continuous. We numerically determine the deconfined quantum critical point and the associated correlation length critical exponent from the finite-size scaling theory of the fidelity susceptibility. Our results are consistent with recent results obtained directly from the matrix product states for infinite-size lattices using others observables. Our work provides a useful probe to study critical behaviors at deconfined quantum critical point from the concept of quantum information.
The out-of-time-ordered correlator (OTOC) is central to the understanding of information scrambling in quantum many-body systems. In this work, we show that the OTOC in a quantum many-body system close to its critical point obeys dynamical scaling la
ws which are specified by a few universal critical exponents of the quantum critical point. Such scaling laws of the OTOC imply a universal form for the butterfly velocity of a chaotic system in the quantum critical region and allow one to locate the quantum critical point and extract all universal critical exponents of the quantum phase transitions. We numerically confirm the universality of the butterfly velocity in a chaotic model, namely the transverse axial next-nearest-neighbor Ising model, and show the feasibility of extracting the critical properties of quantum phase transitions from OTOC using the Lipkin-Meshkov-Glick (LMG) model.
A critically enhanced decay of the Loschmidt echo is characteristic of sudden quench dynamics near a quantum phase transition. Here, we demonstrate that the decay and revival of the Loschmidt echo follows power-law scaling in the system size and the
distance from a critical point with equilibrium critical exponents. We reveal such dynamical scaling laws by analyzing relevant perturbations to the Loschmidt echo cast in a scaling invariant form. We confirm the validity and the generality of the predicted dynamical scaling laws with a diverse range of critical models such as Ising spin models with a short and long range interaction, a finite-component system phase transition, and a topological phase transition. Moreover, using the integrability of systems in the thermodynamic limit, we derive such scaling laws analytically from a microscopic analysis. Our finding promotes the Loschmidt echo to a quantitative non-equilibrium probe of criticality and allows for quantitative predictions on the role of criticality on various physical scenarios where the Loschmidt echo is central to describing non-equilibrium dynamics.
We investigate quantum phase transitions in one-dimensional quantum disordered lattice models, the Anderson model and the Aubry-Andr{e} model, from the fidelity susceptibility approach. First, we find that the fidelity susceptibility and the generali
zed adiabatic susceptibility are maximum at the quantum critical points of the disordered models, through which one can locate the quantum critical point in disordered lattice models. Second, finite-size scaling analysis of the fidelity susceptibility and of the generalized adiabatic susceptibility show that the correlation length critical exponent and the dynamical critical exponent at the quantum critical point of the one-dimensional Anderson model are respectively 2/3 and 2 and of the Aubry-Andr{e} model are respectively 1 and 2.375. Thus the quantum phase transitions in the Anderson model and in the Aubry-Andr{e} model are of different universality classes. Because the fidelity susceptibility and the generalized adiabatic susceptibility are directly connected to the dynamical structure factor which are experimentally accessible in the linear response regime, the fidelity susceptibility in quantum disordered systems may be observed experimentally in near future.
In this work, we establish a general theory of phase transitions and quantum entanglement in the equilibrium state at arbitrary temperatures. First, we derived a set of universal functional relations between the matrix elements of two-body reduced de
nsity matrix of the canonical density matrix and the Helmholtz free energy of the equilibrium state, which implies that the Helmholtz free energy and its derivatives are directly related to entanglement measures because any entanglement measures are defined as a function of the reduced density matrix. Then we show that the first order phase transitions are signaled by the matrix elements of reduced density matrix while the second order phase transitions are witnessed by the first derivatives of the reduced density matrix elements. Near second order phase transition point, we show that the first derivative of the reduced density matrix elements present universal scaling behaviors. Finally we establish a theorem which connects the phase transitions and entanglement at arbitrary temperatures. Our general results are demonstrated in an experimentally relevant many-body spin model.
In this work, we investigate the heat exchange between two quantum systems whose initial equilibrium states are described by the generalized Gibbs ensemble. First, we generalize the fluctuation relations for heat exchange discovered by Jarzynski and
Wojcik to quantum systems prepared in the equilibrium states described by the generalized Gibbs ensemble at different generalized temperatures. Second, we extend the connections between heat exchange and Renyi divergences to quantum systems with very general initial conditions.These relations are applicable for quantum systems with conserved quantities and are universally valid for quantum systems in the integrable and chaotic regimes.
In this work, we establish an exact relation which connects the heat exchange between two systems initialized in their thermodynamic equilibrium states at different temperatures and the R{e}nyi divergences between the initial thermodynamic equilibriu
m state and the final non-equilibrium state of the total system. The relation tells us that the various moments of the heat statistics are determined by the Renyi divergences between the initial equilibrium state and the final non-equilibrium state of the global system. In particular the average heat exchange is quantified by the relative entropy between the initial equilibrium state and the final non-equilibrium state of the global system. The relation is applicable to both finite classical systems and finite quantum systems.
