Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2009.09008 · Physical review. B./Physical review. B

Floquet dynamical quantum phase transition in the extended XY model: Nonadiabatic to adiabatic topological transition

Sara Zamani, Rouhollah Jafari, A. Langari

Published Oct 29, 2020• 71 citations
arXivHTMLPDF

Abstract

We investigate both pure and mixed states Floquet dynamical quantum phase transition (DQPT) in the periodically time-dependent extended XY model. We exactly show that the proposed Floquet Hamiltonian of interacting spins can be expressed as a sum of noninteracting quasispins imposed by an effective time dependent magnetic field (Schwinger-Rabi model). The calculated Chern number indicates that there is a topological transition from the nonadiabatic to adiabatic regime. In the adiabatic regime, the quasispins trace the time dependent effective magnetic field and then oscillate between spin up and down states. While in the nonadiabatic regime, the quasispins cannot follow the time dependent effective magnetic field and feel an average magnetic field. We find the range of driving frequency over which the quasispins experience adiabatic cyclic processes. Moreover, we obtain the exact expression of the Loschmidt amplitude and generalized Loschmidt amplitude of the proposed Floquet system. The results represent that both pure and mixed states dynamical phase transition occurs when the system evolves adiabatically. In other words, the minimum required driving frequency for the appearance of Floquet DQPT is equal to the threshold frequency needed for transition from the nonadiabatic to adiabatic regime.

DOI
10.1103/physrevb.102.144306

Related papers

Dissipative Floquet dynamical quantum phase transition

J. Naji, Masoud Jafari, Rouhollah Jafari +1 more

Non-Hermitian Hamiltonians provide a simple picture for inspecting dissipative systems with natural or induced gain and loss. We investigate the Floquet dynamical phase transition in the dissipative periodically time-driven XY and extended XY models, where the imaginary terms represent the physical gain and loss during the interacting processes with the environment. The time-independent effective Floquet non-Hermitian Hamiltonians disclose three regions by analyzing the non-Hermitian gap: pure real gap (real eigenvalues), pure imaginary gap, and complex gap. We show that each region of the system can be distinguished by the complex geometrical nonadiabatic phase. We have discovered that in the presence of dissipation, the Floquet dynamical phase transitions (FDPTs) still exist in the region where the time-independent effective Floquet non-Hermitian Hamiltonians reveal real eigenvalues. Opposed to expectations based on earlier works on quenched systems, our findings show that the existence of the non-Hermitian topological phase is not an essential condition for dissipative FDPTs (DFDPTs). We also demonstrate the range of driven frequency, over which the DFDPTs occur, narrows down by increasing the dissipation coupling and shrinks to a single point at the critical value of dissipation. Moreover, quantization and jumps of the dynamical geometric phase reveals the topological characteristic feature of DFDPTs in the real gap region where confined to exceptional points.

arXiv:2111.06131•Physical Review A•Feb 28, 2022•44 citations

Floquet dynamical phase transition and entanglement spectrum

Rouhollah Jafari, Alireza Akbari

We explore both pure and mixed state Floquet dynamical quantum phase transitions (FDQFTs) in the one-dimensional $p$-wave superconductor with a time-driven pairing phase. In the Fourier space the model is recast to the noninteracting quasispins subjected to a time-dependent effective magnetic field. We show that FDQFTs occur within a range of driving frequency without resorting to any quenches. Moreover, FDQFTs appear in the region where quasispins are in the resonance regime. In the resonance regime, the population completely cycles the population between the spin down and up states. Additionally, we study the conditions for the appearance of FDQFTs using the entanglement spectrum and purity entanglement measure. Our results imply that the entanglement spectrum can truly capture the resonance regime where FDQFTs occur. Particularly, the dynamical topological region results in the degeneracy of the entanglement spectrum. It is shown that the boundary of the driven frequency range, over which the system reveals FDQFTs, is signaled by the purity entanglement measure.

arXiv:2009.09484•Physical Review A•Jan 8, 2021•75 citations

Floquet dynamical quantum phase transitions

Kai Yang, Longwen Zhou, Wenchao Ma +8 more

Dynamical quantum phase transitions (DQPTs) are manifested by time-domain nonanalytic behaviors of many-body systems. Introducing a quench is so far understood as a typical scenario to induce DQPTs. In this work, we discover a type of DQPTs, termed Floquet DQPTs, as intrinsic features of time-periodic systems. Floquet DQPTs occur within each period of continuous driving, without the need for any quenches. In particular, in a harmonically driven spin chain model, we find analytically the existence of Floquet DQPTs in and only in a parameter regime hosting a certain nontrivial Floquet topological phase. The Floquet DQPTs are further characterized by a dynamical topological invariant defined as the winding number of the Pancharatnam geometric phase versus quasimomentum. These findings are experimentally demonstrated with a single spin in diamond. This work thus opens a door for future studies of DQPTs in connection with topological matter.

arXiv:1901.10365•Physical review. B./Physical review. B•Aug 28, 2019•108 citations

Engineering Floquet dynamical quantum phase transitions

J. Naji, Rouhollah Jafari, Longwen Zhou +1 more

Floquet dynamical quantum phase transitions (FDQPTs) are signified by recurrent nonanalytic behaviors of observables in time. In this work, we introduce a quench-free and generic approach to engineer and control FDQPTs for both pure and mixed Floquet states. By applying time-periodic modulations with two driving frequencies to a general class of spin chain model, we find multiple FDQPTs within each driving period. The model is investigated with equal, commensurate and incommensurate driving frequencies. The nonanalytic cusps of return probability form sublattice structures in time domain. Notably, the number and time locations of these cusps can be flexibly controlled by tuning the Hamiltonian parameter and the frequencies of the drive. We further employ the dynamical topological order parameter, which shows a quantized jump whenever a DQPT happens, to identify the topological feature of FDQPTs. Our findings reveal the advantage of engineering nonequilibrium phase transitions with multifrequency driving fields.

arXiv:2206.03147•Physical review. B./Physical review. B•Sep 28, 2022•37 citations

Dissipative Floquet Dynamical Phase Transition

J. Naji, Masoud Jafari, Rouhollah Jafari +1 more

Non-Hermitian Hamiltonians provide a simple picture for inspecting dissipative systems with natural or induced gain and loss. We investigate the Floquet dynamical phase transition in the dissipative periodically time driven XY and extended XY models, where the imaginary terms represent the physical gain and loss during the interacting processes with the environment. The time-independent effective Floquet non-Hermitian Hamiltonians disclose three regions by analyzing the non-Hermitian gap: pure real gap (real eigenvalues), pure imaginary gap, and complex gap. We show that each region of the system can be distinguished by the complex geometrical non-adiabatic phase. We have discovered that in the presence of dissipation, the Floquet dynamical phase transitions (FDPTs) still exist in the region where the time-independent effective Floquet non-Hermitian Hamiltonians reveal real eigenvalues. Opposed to expectations based on earlier works on quenched systems, our findings show that the existence of the non-Hermitian topological phase is not an essential condition for dissipative FDPTs (DFDPTs). We also demonstrate the range of driven frequency, over which the DFDPTs occur, narrows down by increasing the dissipation coupling and shrinks to a single point at the critical value of dissipation. Moreover, quantization and jumps of the dynamical geometric phase reveals the topological characteristic feature of DFDPTs in the real gap region where confined to exceptional points.

•Nov 11, 2021•0 citations

Biorthogonal-only Floquet Dynamical Quantum Phase Transitions

Jiangrong Wen, Qidong Yuan, Zi-Xiang Hu +1 more

Non-Hermitian dynamical quantum phase transitions (DQPTs) are intrinsically sensitive to the choice of inner product under nonunitary time evolution. Although the biorthogonal formulation based on associated states provides a normalized Loschmidt echo with a probabilistic interpretation, previous studies have found biorthogonal and self-normal DQPTs to occur in the same parameter regimes, suggesting that the two forms of dynamical criticality are concomitant. Here we demonstrate that this is not the case. In an exactly solvable periodically driven non-Hermitian Su-Schrieffer-Heeger chain, we uncover a finite biorthogonal-only Floquet DQPT regime, where the biorthogonal Loschmidt rate becomes nonanalytic while the self-normal Loschmidt rate remains smooth. The critical conditions are obtained analytically, showing that the onset of biorthogonal Floquet DQPTs is locked to the exceptional lines of the effective Floquet Hamiltonian, whereas self-normal criticality has no corresponding spectral boundary. Moreover, for each critical momentum, the biorthogonal DQPT exhibits a pair of critical times within every driving period, whereas the self-normal DQPT exhibits only one. Our results establish a fundamental distinction between biorthogonal and self-normal DQPTs, thereby opening a route toward new nonequilibrium quantum phenomena in non-Hermitian systems.

quant-pharXiv:2608.07882•Aug 11, 2026•0 citations
We investigate both pure and mixed states Floquet dynamical quantum phase transition (DQPT) in the periodically time-dependent extended XY model. We exactly show that the proposed Floquet Hamiltonian of interacting spins can be expressed as a sum of noninteracting quasispins imposed by an effective time dependent magnetic field (Schwinger-Rabi model). The calculated Chern number indicates that there is a topological transition from the nonadiabatic to adiabatic regime. In the adiabatic regime, the quasispins trace the time dependent effective magnetic field and then oscillate between spin up and down states. While in the nonadiabatic regime, the quasispins cannot follow the time dependent effective magnetic field and feel an average magnetic field. We find the range of driving frequency over which the quasispins experience adiabatic cyclic processes. Moreover, we obtain the exact expression of the Loschmidt amplitude and generalized Loschmidt amplitude of the proposed Floquet system. The results represent that both pure and mixed states dynamical phase transition occurs when the system evolves adiabatically. In other words, the minimum required driving frequency for the appearance of Floquet DQPT is equal to the threshold frequency needed for transition from the nonadiabatic to adiabatic regime.
Non-Hermitian Hamiltonians provide a simple picture for inspecting dissipative systems with natural or induced gain and loss. We investigate the Floquet dynamical phase transition in the dissipative periodically time-driven XY and extended XY models, where the imaginary terms represent the physical gain and loss during the interacting processes with the environment. The time-independent effective Floquet non-Hermitian Hamiltonians disclose three regions by analyzing the non-Hermitian gap: pure real gap (real eigenvalues), pure imaginary gap, and complex gap. We show that each region of the system can be distinguished by the complex geometrical nonadiabatic phase. We have discovered that in the presence of dissipation, the Floquet dynamical phase transitions (FDPTs) still exist in the region where the time-independent effective Floquet non-Hermitian Hamiltonians reveal real eigenvalues. Opposed to expectations based on earlier works on quenched systems, our findings show that the existence of the non-Hermitian topological phase is not an essential condition for dissipative FDPTs (DFDPTs). We also demonstrate the range of driven frequency, over which the DFDPTs occur, narrows down by increasing the dissipation coupling and shrinks to a single point at the critical value of dissipation. Moreover, quantization and jumps of the dynamical geometric phase reveals the topological characteristic feature of DFDPTs in the real gap region where confined to exceptional points.
We explore both pure and mixed state Floquet dynamical quantum phase transitions (FDQFTs) in the one-dimensional ppp-wave superconductor with a time-driven pairing phase. In the Fourier space the model is recast to the noninteracting quasispins subjected to a time-dependent effective magnetic field. We show that FDQFTs occur within a range of driving frequency without resorting to any quenches. Moreover, FDQFTs appear in the region where quasispins are in the resonance regime. In the resonance regime, the population completely cycles the population between the spin down and up states. Additionally, we study the conditions for the appearance of FDQFTs using the entanglement spectrum and purity entanglement measure. Our results imply that the entanglement spectrum can truly capture the resonance regime where FDQFTs occur. Particularly, the dynamical topological region results in the degeneracy of the entanglement spectrum. It is shown that the boundary of the driven frequency range, over which the system reveals FDQFTs, is signaled by the purity entanglement measure.
Dynamical quantum phase transitions (DQPTs) are manifested by time-domain nonanalytic behaviors of many-body systems. Introducing a quench is so far understood as a typical scenario to induce DQPTs. In this work, we discover a type of DQPTs, termed Floquet DQPTs, as intrinsic features of time-periodic systems. Floquet DQPTs occur within each period of continuous driving, without the need for any quenches. In particular, in a harmonically driven spin chain model, we find analytically the existence of Floquet DQPTs in and only in a parameter regime hosting a certain nontrivial Floquet topological phase. The Floquet DQPTs are further characterized by a dynamical topological invariant defined as the winding number of the Pancharatnam geometric phase versus quasimomentum. These findings are experimentally demonstrated with a single spin in diamond. This work thus opens a door for future studies of DQPTs in connection with topological matter.
Floquet dynamical quantum phase transitions (FDQPTs) are signified by recurrent nonanalytic behaviors of observables in time. In this work, we introduce a quench-free and generic approach to engineer and control FDQPTs for both pure and mixed Floquet states. By applying time-periodic modulations with two driving frequencies to a general class of spin chain model, we find multiple FDQPTs within each driving period. The model is investigated with equal, commensurate and incommensurate driving frequencies. The nonanalytic cusps of return probability form sublattice structures in time domain. Notably, the number and time locations of these cusps can be flexibly controlled by tuning the Hamiltonian parameter and the frequencies of the drive. We further employ the dynamical topological order parameter, which shows a quantized jump whenever a DQPT happens, to identify the topological feature of FDQPTs. Our findings reveal the advantage of engineering nonequilibrium phase transitions with multifrequency driving fields.
Non-Hermitian Hamiltonians provide a simple picture for inspecting dissipative systems with natural or induced gain and loss. We investigate the Floquet dynamical phase transition in the dissipative periodically time driven XY and extended XY models, where the imaginary terms represent the physical gain and loss during the interacting processes with the environment. The time-independent effective Floquet non-Hermitian Hamiltonians disclose three regions by analyzing the non-Hermitian gap: pure real gap (real eigenvalues), pure imaginary gap, and complex gap. We show that each region of the system can be distinguished by the complex geometrical non-adiabatic phase. We have discovered that in the presence of dissipation, the Floquet dynamical phase transitions (FDPTs) still exist in the region where the time-independent effective Floquet non-Hermitian Hamiltonians reveal real eigenvalues. Opposed to expectations based on earlier works on quenched systems, our findings show that the existence of the non-Hermitian topological phase is not an essential condition for dissipative FDPTs (DFDPTs). We also demonstrate the range of driven frequency, over which the DFDPTs occur, narrows down by increasing the dissipation coupling and shrinks to a single point at the critical value of dissipation. Moreover, quantization and jumps of the dynamical geometric phase reveals the topological characteristic feature of DFDPTs in the real gap region where confined to exceptional points.
Non-Hermitian dynamical quantum phase transitions (DQPTs) are intrinsically sensitive to the choice of inner product under nonunitary time evolution. Although the biorthogonal formulation based on associated states provides a normalized Loschmidt echo with a probabilistic interpretation, previous studies have found biorthogonal and self-normal DQPTs to occur in the same parameter regimes, suggesting that the two forms of dynamical criticality are concomitant. Here we demonstrate that this is not the case. In an exactly solvable periodically driven non-Hermitian Su-Schrieffer-Heeger chain, we uncover a finite biorthogonal-only Floquet DQPT regime, where the biorthogonal Loschmidt rate becomes nonanalytic while the self-normal Loschmidt rate remains smooth. The critical conditions are obtained analytically, showing that the onset of biorthogonal Floquet DQPTs is locked to the exceptional lines of the effective Floquet Hamiltonian, whereas self-normal criticality has no corresponding spectral boundary. Moreover, for each critical momentum, the biorthogonal DQPT exhibits a pair of critical times within every driving period, whereas the self-normal DQPT exhibits only one. Our results establish a fundamental distinction between biorthogonal and self-normal DQPTs, thereby opening a route toward new nonequilibrium quantum phenomena in non-Hermitian systems.