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:1611.05085 · Physical review. B./Physical review. B

Topology of a dissipative spin: Dynamical Chern number, bath-induced nonadiabaticity, and a quantum dynamo effect

Loïc Henriet, Antonio Sclocchi, Peter P. Orth, Karyn Le Hur

Published Feb 15, 2017• 20 citations
arXivHTMLPDF

Abstract

We analyze the topological deformations of the ground state manifold of a quantum spin-1/2 in a magnetic field $\mathbit{H}=H(sin\ensuremath{\theta}cos\ensuremath{\phi},sin\ensuremath{\theta}sin\ensuremath{\phi},cos\ensuremath{\theta})$ induced by a coupling to an ohmic quantum dissipative environment at zero temperature. From Bethe ansatz results and a variational approach, we confirm that the Chern number associated with the geometry of the reduced spin ground state manifold is preserved in the delocalized phase for $\ensuremath{\alpha}<1$. We report a divergence of the Berry curvature at ${\ensuremath{\alpha}}_{c}=1$ for magnetic fields aligned along the equator $\ensuremath{\theta}=\ensuremath{\pi}/2$. This divergence is caused by the complete quenching of the transverse magnetic field by the bath associated with a gap closing that occurs at the localization Kosterlitz-Thouless quantum phase transition in this model. Recent experiments in quantum circuits have engineered nonequilibrium protocols to access topological properties from a measurement of a dynamical Chern number defined via the out-of-equilibrium spin expectation values. Applying a numerically exact stochastic Schr\"odinger approach we find that, for a fixed field sweep velocity $\ensuremath{\theta}(t)=vt$, the bath induces a crossover from (quasi)adiabatic to nonadiabatic dynamical behavior when the spin bath coupling $\ensuremath{\alpha}$ increases. We also investigate the particular regime $H/{\ensuremath{\omega}}_{c}\ensuremath{\ll}v/H\ensuremath{\ll}1$ with large bath cutoff frequency ${\ensuremath{\omega}}_{c}$, where the dynamical Chern number vanishes already at $\ensuremath{\alpha}=1/2$. In this regime, the mapping to an interacting resonance level model enables us to analytically describe the behavior of the dynamical Chern number in the vicinity of $\ensuremath{\alpha}=1/2$. We further provide an intuitive physical explanation of the bath-induced breakdown of adiabaticity in analogy to the Faraday effect in electromagnetism. We demonstrate that the driving of the spin leads to the production of a large number of bosonic excitations in the bath, which strongly affect the spin dynamics. Finally, we quantify the spin-bath entanglement and formulate an analogy with an effective model at thermal equilibrium.

DOI
10.1103/physrevb.95.054307

Related papers

Disorder in dissipation-induced topological states: Evidence for a different type of localization transition

Alon Beck, Moshe Goldstein

The quest for nonequilibrium quantum phase transitions is often hampered by the tendency of driving and dissipation to give rise to an effective temperature, resulting in classical behavior. Could this be different when the dissipation is engineered to drive the system into a nontrivial quantum coherent steady state? In this work we shed light on this issue by studying the effect of disorder on recently introduced dissipation-induced Chern topological states, and examining the eigenmodes of the Hermitian steady-state density matrix or entanglement Hamiltonian. We find that, similarly to equilibrium, each Landau band has a single delocalized level near its center. However, using three different finite-size scaling methods we show that the critical exponent $\ensuremath{\nu}$ describing the divergence of the localization length upon approaching the delocalized state is significantly different from equilibrium if disorder is introduced into the nondissipative part of the dynamics. This indicates a different type of nonequilibrium quantum critical universality class accessible in cold-atom experiments.

arXiv:2011.09730•Physical review. B./Physical review. B•Jun 1, 2021•20 citations

Measuring the Second Chern Number from Nonadiabatic Effects

Michael Kolodrubetz

The geometry and topology of quantum systems have deep connections to quantum dynamics. In this Letter, I show how to measure the non-Abelian Berry curvature and its related topological invariant, the second Chern number, using dynamical techniques. The second Chern number is the defining topological characteristic of the four-dimensional generalization of the quantum Hall effect and has relevance in systems from three-dimensional topological insulators to Yang-Mills field theory. I illustrate its measurement using the simple example of a spin-3/2 particle in an electric quadrupole field. I show how one can dynamically measure diagonal components of the Berry curvature in an overcomplete basis of the degenerate ground state space and use this to extract the full non-Abelian Berry curvature. I also show that one can accomplish the same ideas by stochastically averaging over random initial states in the degenerate ground state manifold. Finally, I show how this system can be manufactured and the topological invariant measured in a variety of realistic systems, from superconducting qubits to trapped ions and cold atoms.

arXiv:1602.03892•Physical Review Letters•Jun 30, 2016•26 citations

Disorder in dissipation-induced topological states: Evidence for novel localization transition

Alon Beck, Moshe Goldstein

The quest for nonequilibrium quantum phase transitions is often hampered by the tendency of driving and dissipation to give rise to an effective temperature, resulting in classical behavior. In this work we shed new light on this issue by studying the effect of disorder on recently-introduced dissipation-induced Chern topological states, and examining the eigenmodes of the Hermitian steady state density matrix or entanglement Hamiltonian. We find that, similarly to equilibrium, each Landau band has a single delocalized level near its center. However, using three different finite size scaling methods we show that the critical exponent $\nu$ describing the divergence of the localization length upon approaching the delocalized state is significantly different from equilibrium if disorder is introduced into the non-dissipative part of the dynamics. This indicates a new nonequilibrium quantum critical universality class accessible in cold-atom experiments.

•Nov 19, 2020•1 citation

First-order transitions in spin chains coupled to quantum baths

C. A. Perroni, ANTONIO DE CANDIA, V. Cataudella +2 more

We show that tailoring the dissipative environment allows us to change the features of continuous quantum phase transitions and even induce first-order transitions in ferromagnetic spin chains. In particular, using a numerically exact quantum Monte Carlo method for the paradigmatic Ising chain of one-half spins in a transverse magnetic field, we find that spin couplings to local quantum boson baths (in the Ohmic regime) can drive the transition from the second to the first order even for a low dissipation strength. Moreover, using a variational mean-field approach for the treatment of spin-spin and spin-boson interactions, we point out that phase discontinuities are ascribable to a dissipation-induced effective magnetic field which is intrinsically related to the bath quantum fluctuations and vanishes for classical baths. The effective field is able to switch the sign of the magnetization along the direction of spin-spin interactions. The results can be potentially tested in recent quantum simulators and are relevant for quantum sensing since the spin system could not only detect the properties of nonclassical baths, but also the effects of weak magnetic fields.

arXiv:2207.13782•Physical review. B./Physical review. B•Mar 10, 2023•6 citations

Driven dissipative dynamics and topology of quantum impurity systems

Karyn Le Hur, Loïc Henriet, Loïc Herviou +6 more

In this review, we provide an introduction to and an overview of some more recent advances in real-time dynamics of quantum impurity models and their realizations in quantum devices. We focus on the Ohmic spin–boson and related models, which describe a single spin-1/2 coupled with an infinite collection of harmonic oscillators. The topics are largely drawn from our efforts over the past years, but we also present a few novel results. In the first part of this review, we begin with a pedagogical introduction to the real-time dynamics of a dissipative spin at both high and low temperatures. We then focus on the driven dynamics in the quantum regime beyond the limit of weak spin–bath coupling. In these situations, the non-perturbative stochastic Schrödinger equation method is ideally suited to numerically obtain the spin dynamics as it can incorporate bias fields h z ( t ) of arbitrary time-dependence in the Hamiltonian. We present different recent applications of this method: (i) how topological properties of the spin such as the Berry curvature and the Chern number can be measured dynamically, and how dissipation affects the topology and the measurement protocol, (ii) how quantum spin chains can experience synchronization dynamics via coupling with a common bath. In the second part of this review, we discuss quantum engineering of spin–boson and related models in circuit quantum electrodynamics (cQED), quantum electrical circuits, and cold-atoms architectures. In different realizations, the Ohmic environment can be represented by a long (microwave) transmission line, a Luttinger liquid, a one-dimensional Bose–Einstein condensate or a chain of superconducting Josephson junctions. We show that the quantum impurity can be used as a quantum sensor to detect properties of a bath at minimal coupling, and how dissipative spin dynamics can lead to new insight in the Mott–superfluid transition.

arXiv:1702.05135•Comptes Rendus Physique•May 28, 2018•54 citations

Nonequilibrium occupation number and charge susceptibility of a resonance level close to a dissipative quantum phase transition

Chung‐Hou Chung, K. V. P. Latha

Based on the recent paper [Phys. Rev. Lett. 102, 216803 (2009)], we study the nonequilibrium occupation number ${n}_{d}$ and charge susceptibility $\ensuremath{\chi}$ of a resonance level close to dissipative quantum phase transition of the Kosterlitz-Thouless (KT) type between a delocalized phase for weak dissipation and a localized phase for strong dissipation. The resonance level is coupled to two spinless fermionic baths with a finite bias voltage and an Ohmic bosonic bath representing the dissipative environment. The system is equivalent to an effective anisotropic Kondo model out of equilibrium. Within the nonequilibrium renormalization-group approach, we calculate nonequilibrium magnetization $M$ and spin susceptibility $\ensuremath{\chi}$ in the effective Kondo model, corresponding to $2{n}_{d}\ensuremath{-}1$ and $\ensuremath{\chi}$ of a resonance level, respectively. We demonstrate the smearing of the KT transition in the nonequilibrium magnetization $M$ as a function of the effective anisotropic Kondo couplings, in contrast to a perfect jump in $M$ at the transition in equilibrium. In the limit of large bias voltages, we find $M$ and $\ensuremath{\chi}$ at the KT transition and in the localized phase show deviations from the equilibrium Curie-law behavior. As the system gets deeper in the localized phase, both ${n}_{d}\ensuremath{-}1/2$ and $\ensuremath{\chi}$ decrease more rapidly to zero with increasing bias voltages.

arXiv:1002.4038•Physical Review B•Aug 30, 2010•3 citations
We analyze the topological deformations of the ground state manifold of a quantum spin-1/2 in a magnetic field \mathbitH=H(sin\ensuremathθcos\ensuremathϕ,sin\ensuremathθsin\ensuremathϕ,cos\ensuremathθ)\mathbit{H}=H(sin\ensuremath{\theta}cos\ensuremath{\phi},sin\ensuremath{\theta}sin\ensuremath{\phi},cos\ensuremath{\theta})\mathbitH=H(sin\ensuremathθcos\ensuremathϕ,sin\ensuremathθsin\ensuremathϕ,cos\ensuremathθ) induced by a coupling to an ohmic quantum dissipative environment at zero temperature. From Bethe ansatz results and a variational approach, we confirm that the Chern number associated with the geometry of the reduced spin ground state manifold is preserved in the delocalized phase for \ensuremathα<1\ensuremath{\alpha}<1\ensuremathα<1. We report a divergence of the Berry curvature at \ensuremathαc=1{\ensuremath{\alpha}}_{c}=1\ensuremathαc​=1 for magnetic fields aligned along the equator \ensuremathθ=\ensuremathπ/2\ensuremath{\theta}=\ensuremath{\pi}/2\ensuremathθ=\ensuremathπ/2. This divergence is caused by the complete quenching of the transverse magnetic field by the bath associated with a gap closing that occurs at the localization Kosterlitz-Thouless quantum phase transition in this model. Recent experiments in quantum circuits have engineered nonequilibrium protocols to access topological properties from a measurement of a dynamical Chern number defined via the out-of-equilibrium spin expectation values. Applying a numerically exact stochastic Schr"odinger approach we find that, for a fixed field sweep velocity \ensuremathθ(t)=vt\ensuremath{\theta}(t)=vt\ensuremathθ(t)=vt, the bath induces a crossover from (quasi)adiabatic to nonadiabatic dynamical behavior when the spin bath coupling \ensuremathα\ensuremath{\alpha}\ensuremathα increases. We also investigate the particular regime H/\ensuremathωc\ensuremath≪v/H\ensuremath≪1H/{\ensuremath{\omega}}_{c}\ensuremath{\ll}v/H\ensuremath{\ll}1H/\ensuremathωc​\ensuremath≪v/H\ensuremath≪1 with large bath cutoff frequency \ensuremathωc{\ensuremath{\omega}}_{c}\ensuremathωc​, where the dynamical Chern number vanishes already at \ensuremathα=1/2\ensuremath{\alpha}=1/2\ensuremathα=1/2. In this regime, the mapping to an interacting resonance level model enables us to analytically describe the behavior of the dynamical Chern number in the vicinity of \ensuremathα=1/2\ensuremath{\alpha}=1/2\ensuremathα=1/2. We further provide an intuitive physical explanation of the bath-induced breakdown of adiabaticity in analogy to the Faraday effect in electromagnetism. We demonstrate that the driving of the spin leads to the production of a large number of bosonic excitations in the bath, which strongly affect the spin dynamics. Finally, we quantify the spin-bath entanglement and formulate an analogy with an effective model at thermal equilibrium.
The quest for nonequilibrium quantum phase transitions is often hampered by the tendency of driving and dissipation to give rise to an effective temperature, resulting in classical behavior. Could this be different when the dissipation is engineered to drive the system into a nontrivial quantum coherent steady state? In this work we shed light on this issue by studying the effect of disorder on recently introduced dissipation-induced Chern topological states, and examining the eigenmodes of the Hermitian steady-state density matrix or entanglement Hamiltonian. We find that, similarly to equilibrium, each Landau band has a single delocalized level near its center. However, using three different finite-size scaling methods we show that the critical exponent $\ensuremath{\nu}$ describing the divergence of the localization length upon approaching the delocalized state is significantly different from equilibrium if disorder is introduced into the nondissipative part of the dynamics. This indicates a different type of nonequilibrium quantum critical universality class accessible in cold-atom experiments.
The geometry and topology of quantum systems have deep connections to quantum dynamics. In this Letter, I show how to measure the non-Abelian Berry curvature and its related topological invariant, the second Chern number, using dynamical techniques. The second Chern number is the defining topological characteristic of the four-dimensional generalization of the quantum Hall effect and has relevance in systems from three-dimensional topological insulators to Yang-Mills field theory. I illustrate its measurement using the simple example of a spin-3/2 particle in an electric quadrupole field. I show how one can dynamically measure diagonal components of the Berry curvature in an overcomplete basis of the degenerate ground state space and use this to extract the full non-Abelian Berry curvature. I also show that one can accomplish the same ideas by stochastically averaging over random initial states in the degenerate ground state manifold. Finally, I show how this system can be manufactured and the topological invariant measured in a variety of realistic systems, from superconducting qubits to trapped ions and cold atoms.
The quest for nonequilibrium quantum phase transitions is often hampered by the tendency of driving and dissipation to give rise to an effective temperature, resulting in classical behavior. In this work we shed new light on this issue by studying the effect of disorder on recently-introduced dissipation-induced Chern topological states, and examining the eigenmodes of the Hermitian steady state density matrix or entanglement Hamiltonian. We find that, similarly to equilibrium, each Landau band has a single delocalized level near its center. However, using three different finite size scaling methods we show that the critical exponent ν\nuν describing the divergence of the localization length upon approaching the delocalized state is significantly different from equilibrium if disorder is introduced into the non-dissipative part of the dynamics. This indicates a new nonequilibrium quantum critical universality class accessible in cold-atom experiments.
We show that tailoring the dissipative environment allows us to change the features of continuous quantum phase transitions and even induce first-order transitions in ferromagnetic spin chains. In particular, using a numerically exact quantum Monte Carlo method for the paradigmatic Ising chain of one-half spins in a transverse magnetic field, we find that spin couplings to local quantum boson baths (in the Ohmic regime) can drive the transition from the second to the first order even for a low dissipation strength. Moreover, using a variational mean-field approach for the treatment of spin-spin and spin-boson interactions, we point out that phase discontinuities are ascribable to a dissipation-induced effective magnetic field which is intrinsically related to the bath quantum fluctuations and vanishes for classical baths. The effective field is able to switch the sign of the magnetization along the direction of spin-spin interactions. The results can be potentially tested in recent quantum simulators and are relevant for quantum sensing since the spin system could not only detect the properties of nonclassical baths, but also the effects of weak magnetic fields.
In this review, we provide an introduction to and an overview of some more recent advances in real-time dynamics of quantum impurity models and their realizations in quantum devices. We focus on the Ohmic spin–boson and related models, which describe a single spin-1/2 coupled with an infinite collection of harmonic oscillators. The topics are largely drawn from our efforts over the past years, but we also present a few novel results. In the first part of this review, we begin with a pedagogical introduction to the real-time dynamics of a dissipative spin at both high and low temperatures. We then focus on the driven dynamics in the quantum regime beyond the limit of weak spin–bath coupling. In these situations, the non-perturbative stochastic Schrödinger equation method is ideally suited to numerically obtain the spin dynamics as it can incorporate bias fields h z ( t ) of arbitrary time-dependence in the Hamiltonian. We present different recent applications of this method: (i) how topological properties of the spin such as the Berry curvature and the Chern number can be measured dynamically, and how dissipation affects the topology and the measurement protocol, (ii) how quantum spin chains can experience synchronization dynamics via coupling with a common bath. In the second part of this review, we discuss quantum engineering of spin–boson and related models in circuit quantum electrodynamics (cQED), quantum electrical circuits, and cold-atoms architectures. In different realizations, the Ohmic environment can be represented by a long (microwave) transmission line, a Luttinger liquid, a one-dimensional Bose–Einstein condensate or a chain of superconducting Josephson junctions. We show that the quantum impurity can be used as a quantum sensor to detect properties of a bath at minimal coupling, and how dissipative spin dynamics can lead to new insight in the Mott–superfluid transition.
Based on the recent paper [Phys. Rev. Lett. 102, 216803 (2009)], we study the nonequilibrium occupation number nd{n}_{d}nd​ and charge susceptibility $\ensuremath{\chi}$ of a resonance level close to dissipative quantum phase transition of the Kosterlitz-Thouless (KT) type between a delocalized phase for weak dissipation and a localized phase for strong dissipation. The resonance level is coupled to two spinless fermionic baths with a finite bias voltage and an Ohmic bosonic bath representing the dissipative environment. The system is equivalent to an effective anisotropic Kondo model out of equilibrium. Within the nonequilibrium renormalization-group approach, we calculate nonequilibrium magnetization MMM and spin susceptibility $\ensuremath{\chi}$ in the effective Kondo model, corresponding to $2{n}_{d}\ensuremath{-}1$ and $\ensuremath{\chi}$ of a resonance level, respectively. We demonstrate the smearing of the KT transition in the nonequilibrium magnetization MMM as a function of the effective anisotropic Kondo couplings, in contrast to a perfect jump in MMM at the transition in equilibrium. In the limit of large bias voltages, we find MMM and $\ensuremath{\chi}$ at the KT transition and in the localized phase show deviations from the equilibrium Curie-law behavior. As the system gets deeper in the localized phase, both ${n}_{d}\ensuremath{-}1/2$ and $\ensuremath{\chi}$ decrease more rapidly to zero with increasing bias voltages.