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arXiv:2302.08206 · Scientific Reports

Anomalous correlation-induced dynamical phase transitions

Niaz Ali Khan, Pei Wang, Munsif Jan, Gao Xianlong

Published Jun 10, 2023• 21 citations
arXivHTMLPDF

Abstract

The nonanalyticity of the Loschmidt echo at critical times in quantum quenched systems is termed as the dynamical quantum phase transition, extending the notion of quantum criticality to a nonequilibrium scenario. In this paper, we establish a new paradigm of dynamical phase transitions driven by a sudden change in the internal spatial correlations of the disorder potential in a low-dimensional disordered system. The quench dynamics between prequenched pure and postquenched random system Hamiltonian reveals an anomalous dynamical quantum phase transition triggered by an infinite disorder correlation in the modulation potential. The physical origin of the anomalous phenomenon is associated with the overlap between the two distinctly different extended states. Furthermore, we explore the quench dynamics between the prequenched random and postquenched pure system Hamiltonian. Interestingly, the quenched system undergoes dynamical quantum phase transitions for the prequench white-noise potential in the thermodynamic limit. In addition, the quench dynamics also shows a clear signature of the delocalization phase transition in the correlated Anderson model.

DOI
10.1038/s41598-023-36564-9

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The nonanalyticity of the Loschmidt echo at critical times in quantum quenched systems is termed as the dynamical quantum phase transition, extending the notion of quantum criticality to a nonequilibrium scenario. In this paper, we establish a new paradigm of dynamical phase transitions driven by a sudden change in the internal spatial correlations of the disorder potential in a low-dimensional disordered system. The quench dynamics between prequenched pure and postquenched random system Hamiltonian reveals an anomalous dynamical quantum phase transition triggered by an infinite disorder correlation in the modulation potential. The physical origin of the anomalous phenomenon is associated with the overlap between the two distinctly different extended states. Furthermore, we explore the quench dynamics between the prequenched random and postquenched pure system Hamiltonian. Interestingly, the quenched system undergoes dynamical quantum phase transitions for the prequench white-noise potential in the thermodynamic limit. In addition, the quench dynamics also shows a clear signature of the delocalization phase transition in the correlated Anderson model.
In this work we develop the theory of the Loschmidt echo and dynamical phase transitions in noninteracting strongly disordered Fermi systems after a quench. In finite systems the Loschmidt echo displays zeros in the complex time plane that depend on the random potential realization. Remarkably, the zeros coalesce to form a 2D manifold in the thermodynamic limit, atypical for 1D systems, crossing the real axis at a sharply defined critical time. We show that this dynamical phase transition can be understood as a transition in the distribution function of the smallest absolute value of the eigenvalues of the Loschmidt matrix and develop a finite-size scaling theory. Contrary to expectations, the notion of dynamical phase transitions in disordered systems becomes decoupled from the equilibrium Anderson localization transition. Our results highlight the striking qualitative differences of quench dynamics in disordered and nondisordered many-fermion systems.
We study the Loschmidt echo and the dynamical free energy of the Anderson model after a quench of the disorder strength. If the initial state is extended and the eigenstates of the postquench Hamiltonian are strongly localized, we argue that the Loschmidt echo exhibits zeros periodically with the period $2\ensuremath{\pi}/D$, where DDD is the width of spectra. At these zeros, the dynamical free energy diverges in a logarithmic way. We present numerical evidence of our argument in one- and three-dimensional Anderson models. Our findings connect the dynamical quantum phase transitions to the localization-delocalization phase transitions.
We unveil the role of the long-time average of the Loschmidt echo in the characterization of nonequilibrium quantum phase transitions by studying sudden quench processes across quantum phase transitions in various quantum systems. While the dynamical quantum phase transitions are characterized by the emergence of a series of zero points at critical times during time evolution, we demonstrate that nonequilibrium quantum phase transitions can be identified by nonanalyticities in the long-time average of the Loschmidt echo. The nonanalytic behaviors are illustrated by a sharp change in the long-time average of the Loschmidt echo or the corresponding rate function or the emergence of divergence in the second derivative of the rate function when the driving quench parameter crosses the phase transition points. The connection between the second derivative of the rate function and fidelity susceptibility is also discussed.
The existence or absence of nonanalytic cusps in the Loschmidt-echo return rate is traditionally employed to distinguish between a regular dynamical phase (regular cusps) and a trivial phase (no cusps) in quantum spin chains after a global quench. However, numerical evidence in a recent study (J. C. Halimeh and V. Zauner-Stauber, arXiv:1610.02019) suggests that instead of the trivial phase, a distinct anomalous dynamical phase characterized by a novel type of nonanalytic cusps occurs in the one-dimensional transverse-field Ising model when interactions are sufficiently long range. Using an analytic semiclassical approach and exact diagonalization, we show that this anomalous phase also arises in the fully connected case of infinite-range interactions, and we discuss its defining signature. Our results show that the transition from the regular to the anomalous dynamical phase coincides with Z2{\mathbb{Z}}_{2}Z2​-symmetry breaking in the infinite-time limit, thereby showing a connection between two different concepts of dynamical criticality. Our work further expands the dynamical phase diagram of long-range interacting quantum spin chains, and can be tested experimentally in ion-trap setups and ultracold atoms in optical cavities, where interactions are inherently long range.
Dynamical quantum phase transitions (DQPTs) manifested in the nonanalyticities in the temporal evolution of a closed quantum system generated by the time-independent final Hamiltonian, following a quench (or ramping) of a parameter of the Hamiltonian, is an emerging frontier of nonequilibrium quantum dynamics. We, here, introduce the notion of a dynamical topological order parameter (DTOP) that characterizes these DQPTs occurring in quenched (or ramped) two-dimensional closed quantum systems; this is quite a nontrivial generalization of the notion of DTOP introduced in Budich and Heyl [Phys. Rev. B 93, 085416 (2016)] for one-dimensional situations. This DTOP is obtained from the ``gauge-invariant'' Pancharatnam phase extracted from the Loschmidt overlap, i.e., the modulus of the overlap between the initially prepared state and its time-evolved counterpart reached following a temporal evolution generated by the time-independent final Hamiltonian. This generic proposal is illustrated considering DQPTs occurring in the subsequent temporal evolution following a sudden quench of the staggered mass of the topological Haldane model on a hexagonal lattice where it stays fixed to zero or unity and makes a discontinuous jump between these two values at critical times at which DQPTs occur. What is remarkable is that while the topology of the equilibrium model is characterized by the Chern number, the emergent topology associated with the DQPTs is characterized by a generalized winding number.
Dynamical quantum phase transitions (DQPTs), which refer to the criticality in time of a quantum many-body system, have attracted much theoretical and experimental research interest recently. Despite that DQPTs are defined and signaled by the nonanalyticities in the Loschmidt rate, its interrelation with various correlation measures such as the equilibrium order parameters of the system remains unclear. In this work, by considering the quench dynamics in an interacting topological model, we find that the equilibrium order parameters of the model in general exhibit signatures around the DQPT, in the short time regime. The first extrema of the equilibrium order parameters are connected to the first Loschmidt rate peak. By studying the unequal-time two-point correlation, we also find that the correlation between the nearest neighbors decays while that with neighbors further away builds up as time grows in the noninteracting case, and upon the addition of repulsive intracell interactions. On the other hand, the intercell interaction tends to suppress the two-site correlations. These findings could provide us insights into the characteristic of the system around DQPTs, and pave the way to a better understanding of the dynamics in nonequilibrium quantum many-body systems.