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:1710.07646 · Physical review. B./Physical review. B

Ramp and periodic dynamics across non-Ising critical points

Roopayan Ghosh, Arnab Sen, K. Sengupta

Published Jan 22, 2018• 19 citations
arXivHTMLPDF

Abstract

We study ramp and periodic dynamics of ultracold bosons in an one-dimensional (1D) optical lattice which supports quantum critical points separating a uniform and a ${Z}_{3}$ or ${Z}_{4}$ symmetry broken density-wave ground state. Our protocol involves both linear and periodic drives which takes the system from the uniform state to the quantum critical point (for linear drive protocol) or to the ordered state and back (for periodic drive protocols) via controlled variation of a parameter of the system Hamiltonian. We provide exact numerical computation, for finite-size boson chains with $L\ensuremath{\le}24$ using exact diagonalization (ED), of the excitation density $D$, the wave function overlap $F$, and the excess energy $Q$ at the end of the drive protocol. For the linear ramp protocol, we identify the range of ramp speeds for which $D$ and $Q$ show Kibble-Zurek scaling. We find, based on numerical analysis with $L\ensuremath{\le}24$, that such scaling is consistent with that expected from critical exponents of the $q$-state Potts universality class with $q=3,4$. For the periodic protocol, we show that the model displays near-perfect dynamical freezing at specific frequencies; at these frequencies $D,Q\ensuremath{\rightarrow}0$ and $|F|\ensuremath{\rightarrow}1$. We provide a semi-analytic explanation of such freezing behavior and relate this phenomenon to a many-body version of Stuckelberg interference. We suggest experiments which can test our theory.

DOI
10.1103/physrevb.97.014309

Related papers

Ramp and periodic dynamics across critical points with Potts universality class

Roopayan Ghosh, Arnab Sen, K. Sengupta

We study ramp and periodic dynamics of ultracold bosons in an one-dimensional (1D) optical lattice which supports quantum critical points belonging to the Potts universality class. Such critical points separate a uniform and a $Z_3$ or $Z_4$ symmetry broken density-wave ground state. Our protocol involves both linear and periodic drives which takes the system from the uniform to the quantum critical point (for linear drive protocol) or to the ordered state and back (for periodic drive protocols) via controlled variation of a parameter of the system Hamiltonian. We provide exact numerical computation for finite-size boson chains with $L \le 24$ using exact-diagonalization (ED) of the excitation density $D$, the wavefunction overlap $F$, and the excess energy $Q$ at the end of the drive protocol. For the linear ramp protocol, we identify the range of ramp speeds for which $D$ and $Q$ shows Kibble-Zurek scaling and show that such scaling is consistent with that expected from critical exponents of the $q$-state Potts universality class with $q=3,4$. For periodic protocol, we show that the model display near-perfect dynamical freezing at specific frequencies; at these frequencies $D, Q \to 0$ and $|F| \to 1$. We provide a semi-analytic explanation of such freezing behavior and relate this phenomenon to a many-body version of Stuckelberg interference. We suggest experiments which can test our theory.

•Oct 20, 2017•0 citations

Dynamic freezing and defect suppression in the tilted one-dimensional Bose-Hubbard model

Uma Divakaran, K. Sengupta

We study the dynamics of a tilted one-dimensional Bose-Hubbard model for two distinct protocols using numerical diagonalization for a finite sized system ($N\ensuremath{\le}18$). The first protocol involves periodic variation of the effective electric field $E$ seen by the bosons which takes the system twice (per drive cycle) through the intermediate quantum critical point. We show that such a drive leads to nonmonotonic variation of the excitation density $D$ and the wave function overlap $F$ at the end of a drive cycle as a function of the drive frequency ${\ensuremath{\omega}}_{1}$, relate this effect to a generalized version of St\"uckelberg interference phenomenon, and identify special frequencies for which $D$ and $1\ensuremath{-}F$ approach zero leading to near-perfect dynamic freezing phenomenon. The second protocol involves a simultaneous linear ramp of both the electric field $E$ (with a rate ${\ensuremath{\omega}}_{1}$) and the boson hopping parameter $J$ (with a rate ${\ensuremath{\omega}}_{2}$) starting from the ground state for a low effective electric field up to the quantum critical point. We find that both $D$ and the residual energy $Q$ decrease with increasing ${\ensuremath{\omega}}_{2}$; our results thus demonstrate a method of achieving near-adiabatic protocol in an experimentally realizable quantum critical system. We suggest experiments to test our theory.

arXiv:1408.4463•Physical Review B•Nov 19, 2014•38 citations

Nonlinear quantum Kibble-Zurek ramps in open systems at finite temperature

Johannes N. Kriel, Emma C. King, Michael Kastner

We analyze quantum systems under a broad class of protocols in which the temperature and a Hamiltonian control parameter are ramped simultaneously and, in general, in a nonlinear fashion toward a quantum critical point. Using an open-system version of a Kitaev quantum wire as an example, we show that, unlike finite-temperature protocols at fixed temperature, these protocols allow us to probe, in an out-of-equilibrium situation and at finite temperature, the universality class (characterized by the critical exponents $ν$ and $z$) of an equilibrium quantum phase transition at zero temperature. Key to this is the identification of ramps in which both coherent and incoherent parts of the open-system dynamics affect the excitation density in a non-negligible way. We also identify the specific ramps for which subleading corrections to the asymptotic scaling laws are suppressed, which serves as a guide to dynamically probing quantum critical exponents in experimentally realistic finite-temperature situations.

quant-pharXiv:2601.10465•Jan 16, 2026•0 citations

Quantum dynamics of a spin model with an extensive degeneracy

Krishanu Ghosh, Diptiman Sen, K. Sengupta

We study the role played by extensive degeneracy in shaping the nature of the quantum dynamics of a one-dimensional spin model for both ramp and periodic drive protocols. The model displays an extensive degenerate manifold of states for a specific value of one of the parameters of its Hamiltonian. We study a linear ramp which takes the spin model through this degenerate point and show that it leads to a deviation from the usual Kibble-Zurek behavior. We also study the Stückelberg oscillations in such a model for a ramp which passes twice through the degenerate point. Our study indicates that such oscillations are strongly suppressed leading to a distinct behavior compared to those arising from double passage through a quantum critical point. Finally, we study the periodic dynamics of the model and show, for a large drive amplitude, the existence of special drive frequencies at which the system exhibits an approximate emergent $U(1)$ symmetry. We study the effect of this emergent symmetry on the correlators of the driven system and demonstrate the existence of dynamic symmetry restoration at these frequencies. We study the fate of the emergent symmetry when the drive amplitude is decreased and discuss possible experiments to test our theory.

arXiv:2502.07609•Physical review. B./Physical review. B•Jun 23, 2025•0 citations

Universality and Dynamic Localization in Kibble-Zurek of the Quantum Ising Model

Michael Kolodrubetz

Recent work has suggested that the Kibble-Zurek mechanism can be re-interpreted as a theory of critical scaling out of equilibrium. While this has been shown for some classical and integrable models, in this work we demonstrate one crucial aspect of critical scaling theory: universality. We solve for the time-dependent finite-size scaling functions of the 1D transversefield Ising chain during a linear-in-time ramp of the field through the quantum critical point. We then simulate Mott-insulating bosons in a tilted potential, an experimentally-studied system in the same equilibrium universality class, and demonstrate that universality holds for the dynamics as well. We find qualitatively athermal features of the scaling functions, such as negative spin correlations, and show that they should be robustly observable within present cold atom experiments. In addition, we discuss recent results in which the Ising model is extended by imbuing the magnetic field with dynamics. We predict using Kibble-Zurek scaling and numerically confirm that the magnetic field ramp is dynamically arrested at the quantum critical point. Extensions of this theory indicate that dynamic localization near critical points should be omnipresent in nature, and may have implications in particle physics as a possible mechanism for giving the Higgs boson a light mass.

Bulletin of the American Physical Society•Mar 7, 2014•0 citations

Dynamics-induced freezing of strongly correlated ultracold bosons

S. Mondal, D. Pekker, K. Sengupta

We study the non-equilibrium dynamics of ultracold bosons in an optical lattice with a time dependent hopping amplitude J(t)=J_0 +δJ \cos(ωt) which takes the system from a superfluid phase near the Mott-superfluid transition (J= J_0+δJ) to a Mott phase (J=J_0-δJ) and back through a quantum critical point (J=J_c) and demonstrate dynamic freezing of the boson wavefunction at specific values of ω. At these values, the wavefunction overlap F (defect density P=1-F) approaches unity (zero). We provide a qualitative explanation of the freezing phenomenon, show it's robustness against quantum fluctuations and the presence of a trap, compute residual energy and superfluid order parameter for such dynamics, and suggest experiments to test our theory.

arXiv:1204.6331•Europhysics Letters (EPL)•Dec 1, 2012•52 citations
We study ramp and periodic dynamics of ultracold bosons in an one-dimensional (1D) optical lattice which supports quantum critical points separating a uniform and a Z3{Z}_{3}Z3​ or Z4{Z}_{4}Z4​ symmetry broken density-wave ground state. Our protocol involves both linear and periodic drives which takes the system from the uniform state to the quantum critical point (for linear drive protocol) or to the ordered state and back (for periodic drive protocols) via controlled variation of a parameter of the system Hamiltonian. We provide exact numerical computation, for finite-size boson chains with L\ensuremath≤24L\ensuremath{\le}24L\ensuremath≤24 using exact diagonalization (ED), of the excitation density DDD, the wave function overlap FFF, and the excess energy QQQ at the end of the drive protocol. For the linear ramp protocol, we identify the range of ramp speeds for which DDD and QQQ show Kibble-Zurek scaling. We find, based on numerical analysis with L\ensuremath≤24L\ensuremath{\le}24L\ensuremath≤24, that such scaling is consistent with that expected from critical exponents of the qqq-state Potts universality class with q=3,4q=3,4q=3,4. For the periodic protocol, we show that the model displays near-perfect dynamical freezing at specific frequencies; at these frequencies D,Q\ensuremath→0D,Q\ensuremath{\rightarrow}0D,Q\ensuremath→0 and ∣F∣\ensuremath→1|F|\ensuremath{\rightarrow}1∣F∣\ensuremath→1. We provide a semi-analytic explanation of such freezing behavior and relate this phenomenon to a many-body version of Stuckelberg interference. We suggest experiments which can test our theory.
We study ramp and periodic dynamics of ultracold bosons in an one-dimensional (1D) optical lattice which supports quantum critical points belonging to the Potts universality class. Such critical points separate a uniform and a Z3Z_3Z3​ or Z4Z_4Z4​ symmetry broken density-wave ground state. Our protocol involves both linear and periodic drives which takes the system from the uniform to the quantum critical point (for linear drive protocol) or to the ordered state and back (for periodic drive protocols) via controlled variation of a parameter of the system Hamiltonian. We provide exact numerical computation for finite-size boson chains with L≤24L \le 24L≤24 using exact-diagonalization (ED) of the excitation density DDD, the wavefunction overlap FFF, and the excess energy QQQ at the end of the drive protocol. For the linear ramp protocol, we identify the range of ramp speeds for which DDD and QQQ shows Kibble-Zurek scaling and show that such scaling is consistent with that expected from critical exponents of the qqq-state Potts universality class with q=3,4q=3,4q=3,4. For periodic protocol, we show that the model display near-perfect dynamical freezing at specific frequencies; at these frequencies D,Q→0D, Q \to 0D,Q→0 and ∣F∣→1|F| \to 1∣F∣→1. We provide a semi-analytic explanation of such freezing behavior and relate this phenomenon to a many-body version of Stuckelberg interference. We suggest experiments which can test our theory.
We study the dynamics of a tilted one-dimensional Bose-Hubbard model for two distinct protocols using numerical diagonalization for a finite sized system ($N\ensuremath{\le}18$). The first protocol involves periodic variation of the effective electric field EEE seen by the bosons which takes the system twice (per drive cycle) through the intermediate quantum critical point. We show that such a drive leads to nonmonotonic variation of the excitation density DDD and the wave function overlap FFF at the end of a drive cycle as a function of the drive frequency ${\ensuremath{\omega}}_{1}$, relate this effect to a generalized version of St\"uckelberg interference phenomenon, and identify special frequencies for which DDD and $1\ensuremath{-}F$ approach zero leading to near-perfect dynamic freezing phenomenon. The second protocol involves a simultaneous linear ramp of both the electric field EEE (with a rate ${\ensuremath{\omega}}_{1}$) and the boson hopping parameter JJJ (with a rate ${\ensuremath{\omega}}_{2}$) starting from the ground state for a low effective electric field up to the quantum critical point. We find that both DDD and the residual energy QQQ decrease with increasing ${\ensuremath{\omega}}_{2}$; our results thus demonstrate a method of achieving near-adiabatic protocol in an experimentally realizable quantum critical system. We suggest experiments to test our theory.
We analyze quantum systems under a broad class of protocols in which the temperature and a Hamiltonian control parameter are ramped simultaneously and, in general, in a nonlinear fashion toward a quantum critical point. Using an open-system version of a Kitaev quantum wire as an example, we show that, unlike finite-temperature protocols at fixed temperature, these protocols allow us to probe, in an out-of-equilibrium situation and at finite temperature, the universality class (characterized by the critical exponents ννν and zzz) of an equilibrium quantum phase transition at zero temperature. Key to this is the identification of ramps in which both coherent and incoherent parts of the open-system dynamics affect the excitation density in a non-negligible way. We also identify the specific ramps for which subleading corrections to the asymptotic scaling laws are suppressed, which serves as a guide to dynamically probing quantum critical exponents in experimentally realistic finite-temperature situations.
We study the role played by extensive degeneracy in shaping the nature of the quantum dynamics of a one-dimensional spin model for both ramp and periodic drive protocols. The model displays an extensive degenerate manifold of states for a specific value of one of the parameters of its Hamiltonian. We study a linear ramp which takes the spin model through this degenerate point and show that it leads to a deviation from the usual Kibble-Zurek behavior. We also study the Stückelberg oscillations in such a model for a ramp which passes twice through the degenerate point. Our study indicates that such oscillations are strongly suppressed leading to a distinct behavior compared to those arising from double passage through a quantum critical point. Finally, we study the periodic dynamics of the model and show, for a large drive amplitude, the existence of special drive frequencies at which the system exhibits an approximate emergent U(1)U(1)U(1) symmetry. We study the effect of this emergent symmetry on the correlators of the driven system and demonstrate the existence of dynamic symmetry restoration at these frequencies. We study the fate of the emergent symmetry when the drive amplitude is decreased and discuss possible experiments to test our theory.
Recent work has suggested that the Kibble-Zurek mechanism can be re-interpreted as a theory of critical scaling out of equilibrium. While this has been shown for some classical and integrable models, in this work we demonstrate one crucial aspect of critical scaling theory: universality. We solve for the time-dependent finite-size scaling functions of the 1D transversefield Ising chain during a linear-in-time ramp of the field through the quantum critical point. We then simulate Mott-insulating bosons in a tilted potential, an experimentally-studied system in the same equilibrium universality class, and demonstrate that universality holds for the dynamics as well. We find qualitatively athermal features of the scaling functions, such as negative spin correlations, and show that they should be robustly observable within present cold atom experiments. In addition, we discuss recent results in which the Ising model is extended by imbuing the magnetic field with dynamics. We predict using Kibble-Zurek scaling and numerically confirm that the magnetic field ramp is dynamically arrested at the quantum critical point. Extensions of this theory indicate that dynamic localization near critical points should be omnipresent in nature, and may have implications in particle physics as a possible mechanism for giving the Higgs boson a light mass.
We study the non-equilibrium dynamics of ultracold bosons in an optical lattice with a time dependent hopping amplitude J(t)=J_0 +δJ \cos(ωt) which takes the system from a superfluid phase near the Mott-superfluid transition (J= J_0+δJ) to a Mott phase (J=J_0-δJ) and back through a quantum critical point (J=J_c) and demonstrate dynamic freezing of the boson wavefunction at specific values of ω. At these values, the wavefunction overlap F (defect density P=1-F) approaches unity (zero). We provide a qualitative explanation of the freezing phenomenon, show it's robustness against quantum fluctuations and the presence of a trap, compute residual energy and superfluid order parameter for such dynamics, and suggest experiments to test our theory.