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:1108.4611 · Physical Review Letters

Geometric Phase Contribution to Quantum Nonequilibrium Many-Body Dynamics

Michael Tomka, Anatoli Polkovnikov, Vladimir Gritsev

Published Feb 23, 2012• 19 citations
arXivHTMLPDF

Abstract

We study the influence of geometry of quantum systems underlying space of states on its quantum many-body dynamics. We observe an interplay between dynamical and topological ingredients of quantum nonequilibrium dynamics revealed by the geometrical structure of the quantum space of states. As a primary example we use the anisotropic XY ring in a transverse magnetic field with an additional time-dependent flux. In particular, if the flux insertion is slow, nonadiabatic transitions in the dynamics are dominated by the dynamical phase. In the opposite limit geometric phase strongly affects transition probabilities. This interplay can lead to a nonequilibrium phase transition between these two regimes. We also analyze the effect of geometric phase on defect generation during crossing a quantum-critical point.

DOI
10.1103/physrevlett.108.080404

Related papers

Information Geometry in Time Dependent Quantum Systems and the Geometric Phase

Anshuman Dey, Suvankar Paul, Pratim Roy +1 more

We study information theoretic geometry in time dependent quantum mechanical systems. First, we discuss global properties of the parameter manifold for two level systems exemplified by i) Rabi oscillations and ii) quenching dynamics of the XY spin chain in a transverse magnetic field, when driven across anisotropic criticality. Next, we comment upon the nature of the geometric phase from classical holonomy analyses of such parameter manifolds. In the context of the transverse XY model in the thermodynamic limit, our results are in contradiction to those in the existing literature, and we argue why the issue deserves a more careful analysis. Finally, we speculate on a novel geometric phase in the model, when driven across a quantum critical line.

arXiv:1605.01358•May 4, 2016•0 citations

Berry Phases and Quantum Phase Transitions

Alioscia Hamma

We study the connection between Berry phases and quantum phase transitions of generic quantum many-body systems. Consider sequences of Berry phases associated to sequences of loops in the parameter space whose limit is a point. If the sequence of Berry phases does not converge to zero, then the limit point is a quantum critical point. Quantum critical points are associated to failures of adiabaticity. We discuss the remarkable example of the anisotropic XY spin chain in a transverse magnetic field and detect the XX region of criticality.

arXiv:quant-ph/0602091•Feb 10, 2006•18 citations

Scaling of Geometric Phases Close to the Quantum Phase Transition in the XY Spin Chain

Shi-Liang Zhu

We show that the geometric phase of the ground state in the XY model obeys scaling behavior in the vicinity of a quantum phase transition. In particular we find that the geometric phase is nonanalytical and its derivative with respect to the field strength diverges at the critical magnetic field. Furthermore, the universality in the critical properties of the geometric phase in a family of models is verified. In addition, since the quantum phase transition occurs at a level crossing or avoided level crossing and these level structures can be captured by the Berry curvature, the established relation between the geometric phase and quantum phase transitions is not a specific property of the XY model, but a very general result of many-body systems.

arXiv:cond-mat/0511565•Physical Review Letters•Feb 23, 2006•258 citations

The geometric phase and the dynamics of quantum phase transition induced by a linear quench

Banasri Basu, P Bandyopadhyay

We have analysed here the role of geometric phase in the dynamical mechanism of quantum phase transition in the transverse Ising model. We have investigated the system when it is driven at a fixed rate characterized by a quench time τ q across the critical point from a paramagnetic to ferromagnetic phase. Our argument is based on the fact that the spin fluctuation occurring during the critical slowing down causes a random fluctuation in the ground-state geometric phase at the critical regime. The correlation function of the random geometric phase determines the excitation probability of the quasiparticles, which are excited during the transition from the inital paramagnetic to the ferromagnetic phase. This helps us to evaluate the number density of the kinks formed during the transition, which is found to scale as . In addition, we have also estimated the spin–spin correlation at criticality.

arXiv:1006.5814•Journal of Physics A Mathematical and Theoretical•Aug 12, 2010•3 citations

Geometric phase and quantum phase transition in an inhomogeneous periodic XY spin- 12 model

Yu-Quan Ma, Shu Chen

The notion of geometric phase has been recently introduced to analyze the quantum phase transitions of many-body systems from the geometrical perspective. In this work, we study the geometric phase of the ground state for an inhomogeneous period-two anisotropic $XY$ model in a transverse field. This model encompasses a group of familiar spin models as its special cases and shows a richer critical behavior. The exact solution is obtained by mapping on a fermionic system through the Jordan-Wigner transformation and constructing the relevant canonical transformation to realize the diagonalization of the Hamiltonian coupled in the $k$ space. The results show that there may exist more than one quantum phase transition point at some parameter regions and these transition points correspond to the divergence or extremum properties of the Berry curvature.

arXiv:1209.0099•Physical Review A•Feb 20, 2009•35 citations

Topological phases in adiabatic and nonadiabatic driven systems

Álvaro Gómez-León, Gloria Platero

In this work we study the geometrical and topological properties of nonequilibrium quantum systems driven by ac fields. We consider two tunnel-coupled spin qubits driven by either spatially homogeneous or inhomogeneous ac fields. Our analysis is an extension of the classical model introduced by Berry with the addition of the spatial degree of freedom. We calculate the Berry and Aharonov-Anandan geometric phases, and demonstrate the influence of the different field parameters in the geometric properties. We also discuss the topological properties associated with the different driving regimes, and show that by tuning the different parameters one can induce topological phase transitions, even in the nonadiabatic regime.

arXiv:1209.5305•Physical Review B•Sep 12, 2012•27 citations
We study the influence of geometry of quantum systems underlying space of states on its quantum many-body dynamics. We observe an interplay between dynamical and topological ingredients of quantum nonequilibrium dynamics revealed by the geometrical structure of the quantum space of states. As a primary example we use the anisotropic XY ring in a transverse magnetic field with an additional time-dependent flux. In particular, if the flux insertion is slow, nonadiabatic transitions in the dynamics are dominated by the dynamical phase. In the opposite limit geometric phase strongly affects transition probabilities. This interplay can lead to a nonequilibrium phase transition between these two regimes. We also analyze the effect of geometric phase on defect generation during crossing a quantum-critical point.
We study information theoretic geometry in time dependent quantum mechanical systems. First, we discuss global properties of the parameter manifold for two level systems exemplified by i) Rabi oscillations and ii) quenching dynamics of the XY spin chain in a transverse magnetic field, when driven across anisotropic criticality. Next, we comment upon the nature of the geometric phase from classical holonomy analyses of such parameter manifolds. In the context of the transverse XY model in the thermodynamic limit, our results are in contradiction to those in the existing literature, and we argue why the issue deserves a more careful analysis. Finally, we speculate on a novel geometric phase in the model, when driven across a quantum critical line.
We study the connection between Berry phases and quantum phase transitions of generic quantum many-body systems. Consider sequences of Berry phases associated to sequences of loops in the parameter space whose limit is a point. If the sequence of Berry phases does not converge to zero, then the limit point is a quantum critical point. Quantum critical points are associated to failures of adiabaticity. We discuss the remarkable example of the anisotropic XY spin chain in a transverse magnetic field and detect the XX region of criticality.
We show that the geometric phase of the ground state in the XY model obeys scaling behavior in the vicinity of a quantum phase transition. In particular we find that the geometric phase is nonanalytical and its derivative with respect to the field strength diverges at the critical magnetic field. Furthermore, the universality in the critical properties of the geometric phase in a family of models is verified. In addition, since the quantum phase transition occurs at a level crossing or avoided level crossing and these level structures can be captured by the Berry curvature, the established relation between the geometric phase and quantum phase transitions is not a specific property of the XY model, but a very general result of many-body systems.
We have analysed here the role of geometric phase in the dynamical mechanism of quantum phase transition in the transverse Ising model. We have investigated the system when it is driven at a fixed rate characterized by a quench time τ q across the critical point from a paramagnetic to ferromagnetic phase. Our argument is based on the fact that the spin fluctuation occurring during the critical slowing down causes a random fluctuation in the ground-state geometric phase at the critical regime. The correlation function of the random geometric phase determines the excitation probability of the quasiparticles, which are excited during the transition from the inital paramagnetic to the ferromagnetic phase. This helps us to evaluate the number density of the kinks formed during the transition, which is found to scale as . In addition, we have also estimated the spin–spin correlation at criticality.
The notion of geometric phase has been recently introduced to analyze the quantum phase transitions of many-body systems from the geometrical perspective. In this work, we study the geometric phase of the ground state for an inhomogeneous period-two anisotropic XYXYXY model in a transverse field. This model encompasses a group of familiar spin models as its special cases and shows a richer critical behavior. The exact solution is obtained by mapping on a fermionic system through the Jordan-Wigner transformation and constructing the relevant canonical transformation to realize the diagonalization of the Hamiltonian coupled in the kkk space. The results show that there may exist more than one quantum phase transition point at some parameter regions and these transition points correspond to the divergence or extremum properties of the Berry curvature.
In this work we study the geometrical and topological properties of nonequilibrium quantum systems driven by ac fields. We consider two tunnel-coupled spin qubits driven by either spatially homogeneous or inhomogeneous ac fields. Our analysis is an extension of the classical model introduced by Berry with the addition of the spatial degree of freedom. We calculate the Berry and Aharonov-Anandan geometric phases, and demonstrate the influence of the different field parameters in the geometric properties. We also discuss the topological properties associated with the different driving regimes, and show that by tuning the different parameters one can induce topological phase transitions, even in the nonadiabatic regime.