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:2507.01486 · Physical Review Research

Exactly solvable phase transition in a cavity-coupled one-dimensional Ising chain

Shuntaro Otake, Motoaki Bamba

Published Apr 11, 2026• 1 citation
arXivHTMLPDF

Abstract

Although one-dimensional classical spin chains do not exhibit phase transitions, we found that a phase transition does occur when they are coupled to a cavity photon mode. This provides the simplest exactly solvable examples demonstrating that finite-temperature superradiant phase transitions can emerge from long-range fully connected interactions mediated by photons and interactions within the material.

DOI
10.1103/fxml-nv46

Related papers

Topological Superradiant Universality Classes in Cavity-Mediated Spin Chains

Yunhao Liu, Sheng Yang, Mingyuan Chen +1 more

Superradiant phase transitions are fundamental phenomena in light-matter coupled systems. Here, we uncover a novel class of superradiant criticality that is topologically distinct from previously known superradiant transitions. Using cavity-mediated cluster-Ising chains as an illustrative example, we numerically demonstrate that the critical line separating the superradiant phase from the cavity topological phase hosts robust symmetry-protected edge degeneracies, a feature absent in conventional superradiant transitions. Remarkably, although its local bulk critical properties are indistinguishable from those of the previously identified topologically trivial superradiant transition, the two criticalities cannot be smoothly connected without breaking the protecting symmetries or passing through a multicritical point. We further show that such topological superradiant criticality is generic, also occurring in cavity-mediated $\mathbb{Z}_{n}^{}$ cluster-qudit chains, as supported by complementary lattice simulations.

quant-pharXiv:2610.11495•Oct 9, 2026•0 citations

Quantum phase transition of nonlocal Ising chain with transverse field in a resonator

Yuna Zhang, Xi-Wang Luo, Guang‐Can Guo +2 more

We study the quantum phase transition in a spin chain with variable Ising interactions and position-dependent coupling to a resonator field. Such a complicated model, usually not present in natural physical systems, can be simulated by an array of qubits based on man-made devices and exhibits interesting behavior. We show that, when the coupling between the qubit and field is strong enough, a superradiant phase transition occurs, and it is possible to pick a particular field mode to undergo this phase transition by properly modulating the strength of the Ising interaction. We also study the impact of the resonator field on the magnetic properties of the spin chain and find a rich set of phases characterized by distinctive qubit correlation functions.

arXiv:1409.6468•Physical Review B•Sep 15, 2014•6 citations

(Almost) everything is a Dicke model - Mapping non-superradiant correlated light-matter systems to the exactly solvable Dicke model

Andreas Schellenberger, Kai Phillip Schmidt

We investigate classes of interacting quantum spin systems in a single-mode cavity with a Dicke coupling, as a paradigmatic example of strongly correlated light-matter systems. Coming from the limit of weak light-matter couplings and large number of matter entities, we map the relevant low-energy sector of a broad class of models in the non-superradiant phases onto the exactly solvable Dicke model. We apply the outcomes to the Dicke-Ising model as a paradigmatic example [Phys. Rev. Res. 2, 023131 (2020), Sci. Rep. 4, 4083 (2014)], in agreement with results obtained by mean-field theory [Sci. Rep. 4, 4083 (2014)]. We further accompany and verify our findings with finite-size calculations, using exact diagonalization and the series expansion method pcst ^{++} + + [Phys. Rev. A 108, 013323 (2023)]

arXiv:2402.15209•SciPost Physics Core•Jul 2, 2024•10 citations

Quantum Phase Transition in the Finite Jaynes-Cummings Lattice Systems

Myung-Joong Hwang, Martin Bodo Plenio

Phase transitions are commonly held to occur only in the thermodynamical limit of a large number of system components. Here, we exemplify at the hand of the exactly solvable Jaynes-Cummings (JC) model and its generalization to finite JC lattices that finite component systems of coupled spins and bosons may exhibit quantum phase transitions (QPTs). For the JC model we find a continuous symmetry-breaking QPT, a photonic condensate with a macroscopic occupation as the ground state, and a Goldstone mode as a low-energy excitation. For the two site JC lattice we show analytically that it undergoes a Mott-insulator to superfluid QPT. We identify as the underlying principle of the emergence of finite system QPTs the combination of increasing atomic energy and increasing interaction strength between the atom and the bosonic mode, which allows for the exploration of an increasingly large portion of the infinite dimensional Hilbert space of the bosonic mode. This suggests that finite system phase transitions will be present in a broad range of physical systems.

arXiv:1603.03943•Physical Review Letters•Sep 13, 2016•145 citations

Superradiant phase transitions in one-dimensional correlated Fermi gases with cavity-induced umklapp scattering

Jian-Song Pan

The superradiant phase transitions of one-dimensional correlated Fermi gases in a transversely driven optical cavity, under the umklapp condition that the cavity wave number is equal to two times the Fermi wave number, are studied with bosonization and renormalization group techniques. The bosonization of Fermi fields gives rise to an all-to-all sine-Gordon (SG) model due to the cavity-assisted nonlocal interactions, where the Bose fields at any two spatial points are coupled. The superradiant phase transition is then mapped to the Kosterlitz-Thouless phase transition of the all-to-all SG model. The nesting effect, in which the superradiant phase transition can be triggered by an infinitely small atom-cavity coupling strength, is shown to be preserved for any nonattractive local interactions. For attractive local interactions, the phase transition occurs at a finite critical coupling strength. Nevertheless, the analysis of the scaling dimension indicates that the perturbation of the nonlocal cosine term is indeed relevant (irrelevant) when the scaling dimension is lower (higher) than the critical dimension, similar to the case of an ordinary local SG model. Our work provides an analytical framework for understanding the superradiant phase transitions in low-dimensional correlated intracavity Fermi gases.

arXiv:2109.08368•Physical Review A•Jan 10, 2022•2 citations

Interacting spins in a cavity: Finite-size effects and symmetry-breaking dynamics

Søren Gammelmark, Klaus Mølmer

We calculate the ground state and simulate the dynamics of a finite chain of spins with Ising nearest-neighbor interactions and a Dicke collective spin interaction with a single-mode cavity field. We recover the signatures of first- and second-order phase transitions predicted by mean-field theory, and for small chains, we find significant and nontrivial finite-size effects. Below the first-order phase transition, even quite large spin chains of 30--40 spins give rise to a mean photon number and number fluctuations significantly above the mean-field vacuum result. Near the second-order phase critical point, our calculations reveal photon number fluctuations that grow beyond Poisson statistics with the size of the spin chain. We simulate the stochastic evolution of the system when the cavity output field is subject to homodyne detection. For an initial state close to the first-order phase-transition the random character of the measurement process causes a measurement-induced symmetry breaking in the system. This symmetry breaking occurs on the time scale needed for an observer to gather sufficient information to distinguish between the two possible (mean-field) symmetry-broken states.

arXiv:1202.5397•Physical Review A•Apr 25, 2012•20 citations
Although one-dimensional classical spin chains do not exhibit phase transitions, we found that a phase transition does occur when they are coupled to a cavity photon mode. This provides the simplest exactly solvable examples demonstrating that finite-temperature superradiant phase transitions can emerge from long-range fully connected interactions mediated by photons and interactions within the material.
Superradiant phase transitions are fundamental phenomena in light-matter coupled systems. Here, we uncover a novel class of superradiant criticality that is topologically distinct from previously known superradiant transitions. Using cavity-mediated cluster-Ising chains as an illustrative example, we numerically demonstrate that the critical line separating the superradiant phase from the cavity topological phase hosts robust symmetry-protected edge degeneracies, a feature absent in conventional superradiant transitions. Remarkably, although its local bulk critical properties are indistinguishable from those of the previously identified topologically trivial superradiant transition, the two criticalities cannot be smoothly connected without breaking the protecting symmetries or passing through a multicritical point. We further show that such topological superradiant criticality is generic, also occurring in cavity-mediated Zn\mathbb{Z}_{n}^{}Zn​ cluster-qudit chains, as supported by complementary lattice simulations.
We study the quantum phase transition in a spin chain with variable Ising interactions and position-dependent coupling to a resonator field. Such a complicated model, usually not present in natural physical systems, can be simulated by an array of qubits based on man-made devices and exhibits interesting behavior. We show that, when the coupling between the qubit and field is strong enough, a superradiant phase transition occurs, and it is possible to pick a particular field mode to undergo this phase transition by properly modulating the strength of the Ising interaction. We also study the impact of the resonator field on the magnetic properties of the spin chain and find a rich set of phases characterized by distinctive qubit correlation functions.
We investigate classes of interacting quantum spin systems in a single-mode cavity with a Dicke coupling, as a paradigmatic example of strongly correlated light-matter systems. Coming from the limit of weak light-matter couplings and large number of matter entities, we map the relevant low-energy sector of a broad class of models in the non-superradiant phases onto the exactly solvable Dicke model. We apply the outcomes to the Dicke-Ising model as a paradigmatic example [Phys. Rev. Res. 2, 023131 (2020), Sci. Rep. 4, 4083 (2014)], in agreement with results obtained by mean-field theory [Sci. Rep. 4, 4083 (2014)]. We further accompany and verify our findings with finite-size calculations, using exact diagonalization and the series expansion method pcst ^{++} + + [Phys. Rev. A 108, 013323 (2023)]
Phase transitions are commonly held to occur only in the thermodynamical limit of a large number of system components. Here, we exemplify at the hand of the exactly solvable Jaynes-Cummings (JC) model and its generalization to finite JC lattices that finite component systems of coupled spins and bosons may exhibit quantum phase transitions (QPTs). For the JC model we find a continuous symmetry-breaking QPT, a photonic condensate with a macroscopic occupation as the ground state, and a Goldstone mode as a low-energy excitation. For the two site JC lattice we show analytically that it undergoes a Mott-insulator to superfluid QPT. We identify as the underlying principle of the emergence of finite system QPTs the combination of increasing atomic energy and increasing interaction strength between the atom and the bosonic mode, which allows for the exploration of an increasingly large portion of the infinite dimensional Hilbert space of the bosonic mode. This suggests that finite system phase transitions will be present in a broad range of physical systems.
The superradiant phase transitions of one-dimensional correlated Fermi gases in a transversely driven optical cavity, under the umklapp condition that the cavity wave number is equal to two times the Fermi wave number, are studied with bosonization and renormalization group techniques. The bosonization of Fermi fields gives rise to an all-to-all sine-Gordon (SG) model due to the cavity-assisted nonlocal interactions, where the Bose fields at any two spatial points are coupled. The superradiant phase transition is then mapped to the Kosterlitz-Thouless phase transition of the all-to-all SG model. The nesting effect, in which the superradiant phase transition can be triggered by an infinitely small atom-cavity coupling strength, is shown to be preserved for any nonattractive local interactions. For attractive local interactions, the phase transition occurs at a finite critical coupling strength. Nevertheless, the analysis of the scaling dimension indicates that the perturbation of the nonlocal cosine term is indeed relevant (irrelevant) when the scaling dimension is lower (higher) than the critical dimension, similar to the case of an ordinary local SG model. Our work provides an analytical framework for understanding the superradiant phase transitions in low-dimensional correlated intracavity Fermi gases.
We calculate the ground state and simulate the dynamics of a finite chain of spins with Ising nearest-neighbor interactions and a Dicke collective spin interaction with a single-mode cavity field. We recover the signatures of first- and second-order phase transitions predicted by mean-field theory, and for small chains, we find significant and nontrivial finite-size effects. Below the first-order phase transition, even quite large spin chains of 30--40 spins give rise to a mean photon number and number fluctuations significantly above the mean-field vacuum result. Near the second-order phase critical point, our calculations reveal photon number fluctuations that grow beyond Poisson statistics with the size of the spin chain. We simulate the stochastic evolution of the system when the cavity output field is subject to homodyne detection. For an initial state close to the first-order phase-transition the random character of the measurement process causes a measurement-induced symmetry breaking in the system. This symmetry breaking occurs on the time scale needed for an observer to gather sufficient information to distinguish between the two possible (mean-field) symmetry-broken states.