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:1801.06622 · Physical Review Letters

Selective Transient Cooling by Impulse Perturbations in a Simple Toy Model

Michele Fabrizio

Published May 31, 2018• 17 citations
arXivHTMLPDF

Abstract

We show in a simple exactly solvable toy model that a properly designed impulse perturbation can transiently cool down low-energy degrees of freedom at the expense of high-energy ones that heat up. The model consists of two infinite-range quantum Ising models: one, the high-energy sector, with a transverse field much bigger than the other, the low-energy sector. The finite-duration perturbation is a spin exchange that couples the two Ising models with an oscillating coupling strength. We find a cooling of the low-energy sector that is optimized by the oscillation frequency in resonance with the spin exchange excitation. After the perturbation is turned off, the Ising model with a low transverse field can even develop a spontaneous symmetry breaking despite being initially above the critical temperature.

DOI
10.1103/physrevlett.120.220601

Related papers

Dissipative cooling induced by pulse perturbations

Andrea Kazemi Nava, Michele Fabrizio

We investigate the dynamics brought on by an impulse perturbation in two infinite-range quantum Ising models coupled to each other and to a dissipative bath. We show that, if dissipation is faster the higher the excitation energy, the pulse perturbation cools down the low-energy sector of the system, at the expense of the high-energy one, eventually stabilising a transient symmetry-broken state at temperatures higher than the equilibrium critical one. Such non-thermal quasi-steady state may survive for quite a long time after the pulse, if the latter is properly tailored.

arXiv:2105.01321•SciPost Physics•Jan 11, 2022•10 citations

Three species of Schrödinger cat states in an infinite-range spin model

Bo Zhao, Cotty Kerridge, David A. Huse

We explore a transverse-field Ising model that exhibits both spontaneous symmetry breaking and eigenstate thermalization. Within its ferromagnetic phase, the exact eigenstates of the Hamiltonian of any large but finite-sized system are all Schrödinger cat states: superpositions of states with "up" and "down" spontaneous magnetization. This model exhibits two dynamical phase transitions within its ferromagnetic phase: In the lowest-temperature phase the magnetization can macroscopically oscillate between up and down. The relaxation of the magnetization is always overdamped in the remainder of the ferromagnetic phase, which is divided into phases where the system thermally activates itself over the barrier between the up and down states, and where it quantum tunnels.

arXiv:1310.4992•Physical Review E•Aug 5, 2014•9 citations

Quantum criticality in the infinite-range transverse field Ising model

Nicholas J. Curro, Kaeshav Danesh, Rajiv Ranjan Singh

We study quantum criticality in the infinite range transverse-field Ising model. We find subtle differences with respect to the well-known single-site mean-field theory, especially in terms of gap, entanglement and quantum criticality. The calculations are based on numerical diagonalization of Hamiltonians with up to a few thousand spins. This is made possible by the enhanced symmetries of the model, which divide the Hamiltonian into many block-diagonal sectors. The finite temperature phase diagram and the characteristic jump in heat capacity closely resemble the behavior in mean-field theory. However, unlike mean-field theory where excitations are always gapped, the excitation gap in the infinite range model goes to zero from both the paramagnetic side and from the ferromagnetic side on approach to the quantum critical point. Also, contrary to mean-field theory, at the quantum critical point the quantum Fisher information becomes large, implying long-range multipartite entanglement. We find that the main role of temperature is to shift statistical weights from one conserved sector to another. However, low energy excitations in each sector arise only near the quantum critical point implying that low energy quantum fluctuations can arise only in the vicinity of the quantum critical field where they can persist up to temperatures of order the exchange constant.

arXiv:2408.02789•Physical review. B./Physical review. B•Aug 7, 2024•2 citations

Quantum quench in a driven Ising chain

Neil J. Robinson, Isaac Pérez Castillo, Edgar Guzmán-González

We consider the Ising chain driven by oscillatory transverse magnetic fields. For certain parameter regimes, we reveal a hidden integrable structure in the problem, which allows access to the exact time evolution in this driven quantum system. We compute time-evolved one- and two-point functions following a quench that activates the driving. It is shown that this model does not heat up to infinite temperature, despite the absence of energy conservation, and we further discuss the generalization to a family of driven Hamiltonians that do not appear to suffer heating to infinite temperature, despite the absence of integrability and disorder. The particular model studied in detail also presents a route for realizing exotic physics (in this case, signatures of the ${E}_{8}$ structure associated with perturbing a critical quantum Ising chain with a small longitudinal magnetic field) by suitably tuning the driving frequency. In particular, we numerically confirm that the ratio of the masses of the two lowest meson excitations is given by the golden ratio.

arXiv:2011.14345•Physical review. B./Physical review. B•Apr 19, 2021•4 citations

Dynamical quantum phase transitions and broken-symmetry edges in the many-body eigenvalue spectrum

Giacomo Mazza, Michele Fabrizio

Many-body models undergoing a quantum phase transition to a broken-symmetry phase that survives up to a critical temperature must possess, in the ordered phase, symmetric as well as nonsymmetric eigenstates. We predict, and explicitly show in the fully connected Ising model in a transverse field, that these two classes of eigenstates do not overlap in energy, and therefore that an energy edge exists separating low-energy symmetry-breaking eigenstates from high-energy symmetry-invariant ones. This energy is actually responsible, as we show, for the dynamical phase transition displayed by this model under a sudden large increase of the transverse field. A second situation we consider is the opposite, where the symmetry-breaking eigenstates are those in the high-energy sector of the spectrum, whereas the low-energy eigenstates are symmetric. In that case too a special energy must exist marking the boundary and leading to unexpected out-of-equilibrium dynamical behavior. An example is the fermonic repulsive Hubbard model Hamiltonian $\mathcal{H}$. Exploiting the trivial fact that the high-energy spectrum of $\mathcal{H}$ is also the low-energy one of $\ensuremath{-}\mathcal{H}$, we conclude that the high-energy eigenstates of the Hubbard model are superfluid. Simulating in a time-dependent Gutzwiller approximation the time evolution of a high-energy BCS-like trial wave function, we show that a small superconducting order parameter will actually grow in spite of the repulsive nature of the interaction.

arXiv:1210.2034•Physical Review B•Nov 30, 2012•33 citations

Model study of dissipation in quantum phase transitions

Subhasis Sinha, Sushanta Dattagupta

We consider a prototypical system of an infinite range transverse field Ising model coupled to a bosonic bath. By integrating out the bosonic degrees, an effective anisotropic Heisenberg model is obtained for the spin system. The phase diagram of the latter is calculated as a function of coupling to the heat bath and the transverse magnetic field. Collective excitations at low temeratures are assessed within a spin-wave like analysis that exhibits a vanishing energy gap at the quantum critical point. We also consider another limit where the system reduces to a generalized spin-boson model of two interacting spins. By increasing the coupling strength with the heat bath, the two-spin wavefunction changes from an entangled state to a factorized state of two spins which are aligned along the transverse field. We also discuss the possible realization and application of the model to different physical systems.

arXiv:1104.5306•Apr 28, 2011•0 citations
We show in a simple exactly solvable toy model that a properly designed impulse perturbation can transiently cool down low-energy degrees of freedom at the expense of high-energy ones that heat up. The model consists of two infinite-range quantum Ising models: one, the high-energy sector, with a transverse field much bigger than the other, the low-energy sector. The finite-duration perturbation is a spin exchange that couples the two Ising models with an oscillating coupling strength. We find a cooling of the low-energy sector that is optimized by the oscillation frequency in resonance with the spin exchange excitation. After the perturbation is turned off, the Ising model with a low transverse field can even develop a spontaneous symmetry breaking despite being initially above the critical temperature.
We investigate the dynamics brought on by an impulse perturbation in two infinite-range quantum Ising models coupled to each other and to a dissipative bath. We show that, if dissipation is faster the higher the excitation energy, the pulse perturbation cools down the low-energy sector of the system, at the expense of the high-energy one, eventually stabilising a transient symmetry-broken state at temperatures higher than the equilibrium critical one. Such non-thermal quasi-steady state may survive for quite a long time after the pulse, if the latter is properly tailored.
We explore a transverse-field Ising model that exhibits both spontaneous symmetry breaking and eigenstate thermalization. Within its ferromagnetic phase, the exact eigenstates of the Hamiltonian of any large but finite-sized system are all Schrödinger cat states: superpositions of states with "up" and "down" spontaneous magnetization. This model exhibits two dynamical phase transitions within its ferromagnetic phase: In the lowest-temperature phase the magnetization can macroscopically oscillate between up and down. The relaxation of the magnetization is always overdamped in the remainder of the ferromagnetic phase, which is divided into phases where the system thermally activates itself over the barrier between the up and down states, and where it quantum tunnels.
We study quantum criticality in the infinite range transverse-field Ising model. We find subtle differences with respect to the well-known single-site mean-field theory, especially in terms of gap, entanglement and quantum criticality. The calculations are based on numerical diagonalization of Hamiltonians with up to a few thousand spins. This is made possible by the enhanced symmetries of the model, which divide the Hamiltonian into many block-diagonal sectors. The finite temperature phase diagram and the characteristic jump in heat capacity closely resemble the behavior in mean-field theory. However, unlike mean-field theory where excitations are always gapped, the excitation gap in the infinite range model goes to zero from both the paramagnetic side and from the ferromagnetic side on approach to the quantum critical point. Also, contrary to mean-field theory, at the quantum critical point the quantum Fisher information becomes large, implying long-range multipartite entanglement. We find that the main role of temperature is to shift statistical weights from one conserved sector to another. However, low energy excitations in each sector arise only near the quantum critical point implying that low energy quantum fluctuations can arise only in the vicinity of the quantum critical field where they can persist up to temperatures of order the exchange constant.
We consider the Ising chain driven by oscillatory transverse magnetic fields. For certain parameter regimes, we reveal a hidden integrable structure in the problem, which allows access to the exact time evolution in this driven quantum system. We compute time-evolved one- and two-point functions following a quench that activates the driving. It is shown that this model does not heat up to infinite temperature, despite the absence of energy conservation, and we further discuss the generalization to a family of driven Hamiltonians that do not appear to suffer heating to infinite temperature, despite the absence of integrability and disorder. The particular model studied in detail also presents a route for realizing exotic physics (in this case, signatures of the E8{E}_{8}E8​ structure associated with perturbing a critical quantum Ising chain with a small longitudinal magnetic field) by suitably tuning the driving frequency. In particular, we numerically confirm that the ratio of the masses of the two lowest meson excitations is given by the golden ratio.
Many-body models undergoing a quantum phase transition to a broken-symmetry phase that survives up to a critical temperature must possess, in the ordered phase, symmetric as well as nonsymmetric eigenstates. We predict, and explicitly show in the fully connected Ising model in a transverse field, that these two classes of eigenstates do not overlap in energy, and therefore that an energy edge exists separating low-energy symmetry-breaking eigenstates from high-energy symmetry-invariant ones. This energy is actually responsible, as we show, for the dynamical phase transition displayed by this model under a sudden large increase of the transverse field. A second situation we consider is the opposite, where the symmetry-breaking eigenstates are those in the high-energy sector of the spectrum, whereas the low-energy eigenstates are symmetric. In that case too a special energy must exist marking the boundary and leading to unexpected out-of-equilibrium dynamical behavior. An example is the fermonic repulsive Hubbard model Hamiltonian H\mathcal{H}H. Exploiting the trivial fact that the high-energy spectrum of H\mathcal{H}H is also the low-energy one of $\ensuremath{-}\mathcal{H}$, we conclude that the high-energy eigenstates of the Hubbard model are superfluid. Simulating in a time-dependent Gutzwiller approximation the time evolution of a high-energy BCS-like trial wave function, we show that a small superconducting order parameter will actually grow in spite of the repulsive nature of the interaction.
We consider a prototypical system of an infinite range transverse field Ising model coupled to a bosonic bath. By integrating out the bosonic degrees, an effective anisotropic Heisenberg model is obtained for the spin system. The phase diagram of the latter is calculated as a function of coupling to the heat bath and the transverse magnetic field. Collective excitations at low temeratures are assessed within a spin-wave like analysis that exhibits a vanishing energy gap at the quantum critical point. We also consider another limit where the system reduces to a generalized spin-boson model of two interacting spins. By increasing the coupling strength with the heat bath, the two-spin wavefunction changes from an entangled state to a factorized state of two spins which are aligned along the transverse field. We also discuss the possible realization and application of the model to different physical systems.