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arXiv:1901.00299 · Physical review. B./Physical review. B

Dynamical quantum phase transitions on cross-stitch flat band networks

Tong Liu, Hao Guo

Published Mar 29, 2019• 12 citations
arXivHTMLPDF

Abstract

We study the quench dynamics on cross-stitch flat band networks by a sudden change of the intercell hopping strength $J$. For quench processes with $J$ changing as $J=0\ensuremath{\rightarrow}J\ensuremath{\ne}0$, we give the analytical expression to the Loschmidt echo which possesses a series of zero points at critical times ${t}^{*}$, indicating where the dynamical quantum phase transitions occur. We further study the converse quench process with $J\ensuremath{\ne}0\ensuremath{\rightarrow}J=0$, and find a nontrivial example that the prequench quantum state is not an eigenstate of the post-quench Hamiltonian, whereas the Loschmidt echo $\mathcal{L}(t)\ensuremath{\equiv}1$ during this process. For both situations, these results are also illustrated numerically. Finally, we give a brief discussion on the possible experimental observation of these predictions in the system of ultracold atoms in optical lattices.

DOI
10.1103/physrevb.99.104307

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We study the quench dynamics on cross-stitch flat band networks by a sudden change of the intercell hopping strength JJJ. For quench processes with JJJ changing as J=0\ensuremath→J\ensuremath≠0J=0\ensuremath{\rightarrow}J\ensuremath{\ne}0J=0\ensuremath→J\ensuremath=0, we give the analytical expression to the Loschmidt echo which possesses a series of zero points at critical times t∗{t}^{*}t∗, indicating where the dynamical quantum phase transitions occur. We further study the converse quench process with J\ensuremath≠0\ensuremath→J=0J\ensuremath{\ne}0\ensuremath{\rightarrow}J=0J\ensuremath=0\ensuremath→J=0, and find a nontrivial example that the prequench quantum state is not an eigenstate of the post-quench Hamiltonian, whereas the Loschmidt echo L(t)\ensuremath≡1\mathcal{L}(t)\ensuremath{\equiv}1L(t)\ensuremath≡1 during this process. For both situations, these results are also illustrated numerically. Finally, we give a brief discussion on the possible experimental observation of these predictions in the system of ultracold atoms in optical lattices.
A sudden quantum quench of a Bloch band from one topological phase toward another has been shown to exhibit an intimate connection with the notion of a dynamical quantum phase transition (DQPT), where the returning probability of the quenched state to the initial state-i.e., the Loschmidt echo-vanishes at critical times {t^{*}}. Analytical results to date are limited to two-band models, leaving the exact relation between topology and DQPT unclear. In this Letter, we show that, for a general multiband system, a robust DQPT relies on the existence of nodes (i.e., zeros) in the wave function overlap between the initial band and the postquench energy eigenstates. These nodes are topologically protected if the two participating wave functions have distinctive topological indices. We demonstrate these ideas in detail for both one and two spatial dimensions using a three-band generalized Hofstadter model. We also discuss possible experimental observations.
Dynamical quantum phase transition is a nonstationary analog of the equilibrium quantum phase transitions that may occur after global quenches across a quantum phase transition in systems. In this work, we investigate the quench dynamics of single-particle tight-binding quasiperiodic lattices, where the quenching process originates and terminates within the same phases. Intriguingly, the system under quench dynamics undergoes an energy-dependent dynamical quantum phase transition, characterized by the singularities of the Loschmidt echo in time scale. Specifically, we find disentangling behavior between static and dynamical quantum phase transitions for eigenenergies excluding band edges. Remarkably, the connection between static and dynamical quantum phase transitions does not hold generally for all eigenenergies. Our findings suggest the existence of dynamical phase transitions inside the band energies without crossing the critical point under certain conditions. Our results pave the way to a deeper understanding of the energy-dependent nonequilibrium quench dynamics.
In this Letter it is shown that dynamical quantum phase transitions in Loschmidt echos control the nonequilibrium dynamics of the order parameter after particular quantum quenches in systems with broken-symmetry phases. A direct connection between Loschmidt echos and the order parameter dynamics is established which links nonequilibrium microscopic probabilities to the system's macroscopic dynamical properties. These concepts are illustrated numerically using exact diagonalization for quantum quenches in the XXZ chain with initial Néel states. An outlook is given on how to explore these predictions experimentally with ultracold gases in optical lattices.
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.
Dynamical quantum phase transitions reveal singularities in quench dynamics, characterized by the emergence of Loschmidt echo zeros at critical times, which usually exist only in the thermodynamic limit but are absent in finite-size quantum systems. In this Letter, we propose a theoretical scheme to probe Loschmidt echo zeros in finite-size systems by applying a two-step quenching protocol, which offers an experimentally feasible approach to study Loschmidt echo zeros. Using the transverse Ising model as a test bed, we identify that the exact Loschmidt echo zeros can be always accessed by tuning the quench rate, when the quench is across the phase transition point. The associated rate function displays divergence at critical times, accompanying with the change of the dynamical topological order parameter. The critical times are influenced by the quench rate, system size, and momentum modes, embodying the interplay between finite-size effects and critical dynamics. Moreover, the generality of these observations is further confirmed in the XY and Haldane models.
In most lattice models, the closing of a band gap typically occurs at high-symmetry points in the Brillouin zone. Differently, in the Creutz model---describing a system of spinless fermions hopping on a two-leg ladder pierced by a magnetic field---the gap closing at the quantum phase transition between the two topologically nontrivial phases of the model can be moved by tuning the hopping amplitudes. We take advantage of this property to examine the nonequilibrium dynamics of the model after a sudden quench of the magnetic flux through the plaquettes of the ladder. For a quench to one of the equilibrium quantum critical points, we find that the revival period of the Loschmidt echo---measuring the overlap between initial and time-evolved states---is controlled by the gap closing zero-energy modes. In particular, and contrary to expectations, the revival period of the Loschmidt echo for a finite ladder does not scale linearly with size but exhibits jumps determined by the presence or absence of zero-energy modes. We further investigate the conditions for the appearance of dynamical quantum phase transitions in the model and find that, for a quench to an equilibrium critical point, such transitions occur only for ladders of sizes which host zero-energy modes. Exploiting concepts from quantum thermodynamics, we show that the average work and the irreversible work per lattice site exhibit a weak dependence on the size of the system after a quench across an equilibrium critical point, suggesting that quenching into a different phase induces effective correlations among the particles.