We investigate a generic dynamical theory to characterize by quantum quenches the topological quantum phases defined for the equilibrium ground state and study the emergent topology of quantum dynamics when the quenches start from a deep trivial (far from the phase boundary) or shallow trivial (close to the phase boundary) phase to topological regimes. Two dynamical schemes are examined: One is to characterize topological phases via quantum dynamics induced by a single quench along an arbitrary axis of (pseudo)spin polarization, and the other applies a set of quenches with respect to all (pseudo)spin axes. These two schemes are both built on the so-called dynamical bulk-surface correspondence, which shows that the $d$ -dimensional ( $d\mathrm{D}$ ) topological phases with integer invariants can be characterized by the dynamical topological pattern emerging on particular $(d\ensuremath{-}1)\mathrm{D}$ momentum subspaces called band inversion surfaces (BISs). We show that the first dynamical scheme works for both deep and shallow quenches, while for the second scheme, an emergent topological transition, associated with topological charges crossing BISs, is predicted in the joint quench dynamics. A generic criterion for the emergent transition is precisely obtained. Above the criterion (deep quench regime), quantum dynamics on BISs can directly characterize the topology of the postquench Hamiltonian. Below the criterion (shallow quench regime), the quench dynamics may depict a new dynamical topology; the postquench topology can be characterized by the emergent topological invariant plus the total charges moving outside the region enclosed by BISs. We illustrate our results by numerically calculating the 2D quantum anomalous Hall model, which has been realized in ultracold atoms. This work broadens the way to classify topological phases by nonequilibrium quantum dynamics and is feasible for experimental realization.We investigate a generic dynamical theory to characterize by quantum quenches the topological quantum phases defined for the equilibrium ground state and study the emergent topology of quantum dynamics when the quenches start from a deep trivial (far from the phase boundary) or shallow trivial (close to the phase boundary) phase to topological regimes. Two dynamical schemes are examined: One is to characterize topological phases via quantum dynamics induced by a single quench along an arbitrary axis of (pseudo)spin polarization, and the other applies a set of quenches with respect to all (pseudo)spin axes. These two schemes are both built on the so-called dynamical bulk-surface correspondence, which shows that the $d$-dimensional ($d\mathrm{D}$) topological phases with integer invariants can be characterized by the dynamical topological pattern emerging on particular $(d\ensuremath{-}1)\mathrm{D}$ momentum subspaces called band inversion surfaces (BISs). We show that the first dynamical scheme works for both deep and shallow quenches, while for the second scheme, an emergent topological transition, associated with topological charges crossing BISs, is predicted in the joint quench dynamics. A generic criterion for the emergent transition is precisely obtained. Above the criterion (deep quench regime), quantum dynamics on BISs can directly characterize the topology of the postquench Hamiltonian. Below the criterion (shallow quench regime), the quench dynamics may depict a new dynamical topology; the postquench topology can be characterized by the emergent topological invariant plus the total charges moving outside the region enclosed by BISs. We illustrate our results by numerically calculating the 2D quantum anomalous Hall model, which has been realized in ultracold atoms. This work broadens the way to classify topological phases by nonequilibrium quantum dynamics and is feasible for experimental realization.

arXiv:1907.08840Physical Review ADec 10, 201937 citations

Topological Quantum Phase Transitions and Quench Dynamics

Shiuan-Fan Liou

Jan 1, 20190 citations

Emergent topology and dynamical quantum phase transitions in two-dimensional closed quantum systems

Utso Bhattacharya, Amit Dutta

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) 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.

arXiv:1701.03911Physical review. B./Physical review. BJul 11, 201775 citations

Dynamical classification of topological quantum phases

Lin Zhang, Long Zhang, Sen Niu +1 more

arXiv:1802.10061中国科学通报：英文版Sep 29, 2018150 citations

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

Ryo Okugawa, Hiroki Oshiyama, Masayuki Ohzeki

Dynamical quantum phase transitions (DQPTs) are topologically characterized in quantum quench dynamics in topological systems. In this paper, we study Loschmidt amplitudes and DQPTs in quantum quenches in mirror-symmetric topological phases. Based on the topological classification of mirror-symmetric insulators, we show that mirror symmetry creates symmetry-protected DQPTs. If mirror symmetry is present, topologically robust DQPTs can occur in quantum quenches, even in high-dimensional time-reversal invariant systems. Then, we also show that symmetry-protected DQPTs occur in quenches in two-dimensional chiral-symmetric systems with mirror symmetry. Mirror-symmetry-protected DQPTs can be easily captured by a reduced rate function. Moreover, we introduce dynamical topological order parameters for mirror-symmetry-protected DQPTs. Finally, we demonstrate DQPTs using lattice models for a time-reversal invariant topological crystalline insulator and a higher-order topological insulator.Dynamical quantum phase transitions (DQPTs) are topologically characterized in quantum quench dynamics in topological systems. In this paper, we study Loschmidt amplitudes and DQPTs in quantum quenches in mirror-symmetric topological phases. Based on the topological classification of mirror-symmetric insulators, we show that mirror symmetry creates symmetry-protected DQPTs. If mirror symmetry is present, topologically robust DQPTs can occur in quantum quenches, even in high-dimensional time-reversal invariant systems. Then, we also show that symmetry-protected DQPTs occur in quenches in two-dimensional chiral-symmetric systems with mirror symmetry. Mirror-symmetry-protected DQPTs can be easily captured by a reduced rate function. Moreover, we introduce dynamical topological order parameters for mirror-symmetry-protected DQPTs. Finally, we demonstrate DQPTs using lattice models for a time-reversal invariant topological crystalline insulator and a higher-order topological insulator.

arXiv:2105.12768Physical Review ResearchOct 22, 202121 citations

Dynamical topological quantum phase transitions in a finite-size spin system

Shaoying Yin, Hongchun Sun, Jin‐Liang Guo +2 more

Chinese Journal of PhysicsNov 21, 20251 citation

d

-dimensional (

d\mathrm{D}

) topological phases with integer invariants can be characterized by the dynamical topological pattern emerging on particular $(d\ensuremath{-}1)\mathrm{D}$ momentum subspaces called band inversion surfaces (BISs). We show that the first dynamical scheme works for both deep and shallow quenches, while for the second scheme, an emergent topological transition, associated with topological charges crossing BISs, is predicted in the joint quench dynamics. A generic criterion for the emergent transition is precisely obtained. Above the criterion (deep quench regime), quantum dynamics on BISs can directly characterize the topology of the postquench Hamiltonian. Below the criterion (shallow quench regime), the quench dynamics may depict a new dynamical topology; the postquench topology can be characterized by the emergent topological invariant plus the total charges moving outside the region enclosed by BISs. We illustrate our results by numerically calculating the 2D quantum anomalous Hall model, which has been realized in ultracold atoms. This work broadens the way to classify topological phases by nonequilibrium quantum dynamics and is feasible for experimental realization.