Dynamical quantum phase transitions in Weyl semimetals

Abstract

The quench dynamics in type-I inversion symmetric Weyl semimetals (WSM) are explored in this work which, due to the form of the Hamiltonian, may be readily extended to two-dimensional Chern insulators. We analyze the role of equilibrium topological properties characterized by the Chern number of the pre-quench ground state in dictating the non-equilibrium dynamics of the system, specifically, the emergence of dynamical quantum phase transitions (DQPT). By investigating the ground state fidelity, it is found that a change in the signed Chern number constitutes a sufficient but not necessary condition for the occurrence of DQPTs. Depending on the ratio of the transverse and longitudinal hopping parameters, DQPTs may also be observed for quenches lying entirely within the initial Chern phase. Additionally, we analyze the zeros of the boundary partition function discovering that while the zeros generally form two-dimensional structures resulting in one-dimensional critical times, infinitesimal quenches may lead to one-dimensional zeros with zero-dimensional critical times provided the quench distance scales appropriately with the system size. This is strikingly manifested in the nature of non-analyticies of the dynamical free energy, revealing a logarithmic singularity. In addition, following recent experimental advances in observing the dynamical Fisher zeros of the Loschmidt overlap amplitude through azimuthal Bloch phase vortices by Bloch-state tomography, we rigorously investigate the same in WSMs. Finally, we establish the relationship between the dimension of the critical times and the presence of dynamical vortices, demonstrating that only onedimensional critical times arising from two-dimensional manifolds of zeros of the boundary partition function lead to dynamical vortices.

Signature of quantum phase transition manifested in quantum fidelity at zero and finite temperatures

“…But later it has been shown that there may not be non-analyticity in the rate function versus time plot when the quench is across the critical point or there may be a non-analyticity when the quench is not across the critical point. [44] [39] [45]. We show here that the long time limit of our rate function at the T = 0 shows non-analyticity only if the system is quenched across the critical point.…”

Mirror-symmetry-protected dynamical quantum phase transitions in topological crystalline insulators

“…In addition, we compare mirror-symmetry-protected DQPTs with other topologically robust DQPTs in highdimensional systems. When a system can be seen as a collection of 1D (2D) topological systems, robust DQPTs also occur because winding numbers (Chern numbers) can be defined for general lines (planes) in the BZ [37,38,50]. The band topology originates from translational symmetry.…”

“…Within a quantum quench, while a system is prepared as the ground state of an initial Hamiltonian, the state evolves under a different Hamiltonian with suddenly switched parameters. A dynamical quantum phase transition (DQPT) is also known as a nonequilibrium topological phenomenon induced by quantum quenches [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53].…”

Aperiodic dynamical quantum phase transition in multi-band Bloch Hamiltonian and its origin

“…and others [58][59][60][61][62][63][64][65][66][67][68][69][70][71][72]. Additionally, several experiments have directly observed DQPTs, including trapped ions simulations [73][74][75][76], 53-qubit quantum simulations [77], nuclear magnetic resonance quantum simulators [78], quantum walks of photons [79,80], and spinor condensate simulations [81].…”