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:cond-mat/0406674 · Europhysics Letters (EPL)

Direct equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems: Scaling of entanglement

Jose Reslen, Luis Quiroga, Neil F. Johnson

Published Dec 7, 2004• 73 citations
arXivHTMLPDF

Abstract

We show that the quantum phase transition arising in a standard radiation-matter model (Dicke model) belongs to the same universality class as the infinitely coordinated, transverse-field XY model. The effective qubit-qubit exchange interaction is shown to be proportional to the square of the qubit-radiation coupling. A universal finite-size scaling is derived for the corresponding two-qubit entanglement (concurrence) and a size-consistent effective Hamiltonian is proposed for the qubit subsystem.

DOI
10.1209/epl/i2004-10313-4

Related papers

Once more on the equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems

J.G. Brankov, N. S. Tonchev, Valentin Anatol'evich Zagrebnov

In answer to the replies of Reslen {\it et al} [arXiv: quant-ph/0507164 (2005)], and Liberti and Zaffino [arXiv:cond-mat/0507019, (2005)], we comment once more on the temperature-dependent effective Hamiltonians for the Dicke model derived by them in [Europhys. Lett., {\bf 69} (2005) 8] and [Eur. Phys. J., {\bf 44} (2005) 535], respectively. These approximate Hamiltonians cannot be correct for any finite nonzero temperature because they both violate a rigorous result. The fact that the Dicke model belongs to the universality class of, and its thermodynamics is described by the infinitely coordinated transverse-field XY model is known for more than 30 years.

arXiv:quant-ph/0508039•Aug 4, 2005•0 citations

Comment on equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems

J.G. Brankov, N. S. Tonchev, Valentin Anatol'evich Zagrebnov

In this Comment we show that the temperature-dependent effective Hamiltonian derived by Reslen {\it et al} [Europhys. Lett., {\bf 69} (2005) 8] or that one by Liberti and Zaffino [arXiv:cond-mat/0503742] for the Dicke model cannot be correct for any temperature. They both violate a rigorous result. The former is correct only in the quantum (zero-temperature) limit while the last one only in the classical (infinite temperature) limit. The fact that the Dicke model belongs to the universality class of the infinitely coordinated transverse-field XY model is known for more then 30 years.

arXiv:quant-ph/0506207•Jun 24, 2005•0 citations

Quantum phase diagrams of Dicke-Ising models by a wormhole algorithm

Anja Langheld, Max Hörmann, Kai Phillip Schmidt

We gain quantitative insights on effects of light-matter interactions on correlated quantum matter by quantum Monte Carlo simulations. We introduce a wormhole algorithm for the paradigmatic Dicke-Ising model which combines the light-matter interaction of the Dicke model with Ising interactions. The quantum phase diagrams for ferro- and antiferromagnetic interactions on the chain and the square lattice are determined. The occurring superradiant phase transitions are in the same universality class as the Dicke model, leading to a well-known peculiar finite-size scaling that we elucidate in terms of scaling above the upper critical dimension. For the ferromagnetic case, the transition between the normal and the superradiant phase is of second order with Dicke criticality (first order) for large (small) longitudinal fields separated by a multicritical point. For antiferromagnetic interactions, we establish the light-matter analog of a lattice supersolid with off-diagonal superradiant and diagonal magnetic order and determine the nature of all transition lines. Our achievements allow to quantitatively enter the domain of mesoscopic light-matter systems, which is an increasingly prominent topic at the interface of quantum optics and condensed matter physics.

arXiv:2409.15082•Physical review. B./Physical review. B•Sep 4, 2025•7 citations

Quantum phase transitions in coupled two-level atoms in a single-mode cavity

Qing‐Hu Chen, Tao Liu, Yuyu Zhang +1 more

The dipole-coupled two-level atoms (qubits) in a single-mode resonant cavity are studied by extended bosonic coherent states. The numerical solution is presented. The first-order quantum phase transitions may occur in finite systems, in contrast to the original Dicke model. This system also exhibits a second-order quantum phase transition from the normal to the superradiant phase, as in the original Dicke model. Finite-size scaling for several observables---such as average fidelity susceptibility, order parameter, and concurrence---is performed for different interatomic interactions. The scaling exponents obtained suggest that interatomic interactions do not change the universality class.

arXiv:1008.1093•Physical Review A•Nov 30, 2010•28 citations

Dicke model

Mor M. Roses, Emanuele G. Dalla Torre

The Dicke model is a fundamental model of quantum optics, which describes the interaction between light and matter. In the Dicke model, the light component is described as a single quantum mode, while the matter is described as a set of two-level systems. When the coupling between the light and matter crosses a critical value, the Dicke model shows a mean-field phase transition to a superradiant phase. This transition belongs to the Ising universality class and was realized experimentally in cavity quantum electrodynamics experiments. Although the superradiant transition bears some analogy with the lasing instability, these two transitions belong to different universality classes.

PLoS ONE•Sep 4, 2020•27 citations

Scaling, Entanglement, and Quantum Phase Transitions

Andreas Osterloh

We study the entanglement near a quantum phase transition in a class of exactly solvable one‐dimensional quantum magnets, the anisotropic XY models. The critical behaviour (scaling) is reflected by the derivatives of the bipartite entanglent, quantified by the concurrence. However, we found a profound difference between classical correlation and non‐local quantum correlation: The range of the concurrence is found to behave in a non‐universal way, being extremely short‐ranged for the Ising model. This range tends to infinity towards the isotropic XY model.

AIP conference proceedings•Jan 1, 2003•1 citation
We show that the quantum phase transition arising in a standard radiation-matter model (Dicke model) belongs to the same universality class as the infinitely coordinated, transverse-field XY model. The effective qubit-qubit exchange interaction is shown to be proportional to the square of the qubit-radiation coupling. A universal finite-size scaling is derived for the corresponding two-qubit entanglement (concurrence) and a size-consistent effective Hamiltonian is proposed for the qubit subsystem.
In answer to the replies of Reslen {\it et al} [arXiv: quant-ph/0507164 (2005)], and Liberti and Zaffino [arXiv:cond-mat/0507019, (2005)], we comment once more on the temperature-dependent effective Hamiltonians for the Dicke model derived by them in [Europhys. Lett., {\bf 69} (2005) 8] and [Eur. Phys. J., {\bf 44} (2005) 535], respectively. These approximate Hamiltonians cannot be correct for any finite nonzero temperature because they both violate a rigorous result. The fact that the Dicke model belongs to the universality class of, and its thermodynamics is described by the infinitely coordinated transverse-field XY model is known for more than 30 years.
In this Comment we show that the temperature-dependent effective Hamiltonian derived by Reslen {\it et al} [Europhys. Lett., {\bf 69} (2005) 8] or that one by Liberti and Zaffino [arXiv:cond-mat/0503742] for the Dicke model cannot be correct for any temperature. They both violate a rigorous result. The former is correct only in the quantum (zero-temperature) limit while the last one only in the classical (infinite temperature) limit. The fact that the Dicke model belongs to the universality class of the infinitely coordinated transverse-field XY model is known for more then 30 years.
We gain quantitative insights on effects of light-matter interactions on correlated quantum matter by quantum Monte Carlo simulations. We introduce a wormhole algorithm for the paradigmatic Dicke-Ising model which combines the light-matter interaction of the Dicke model with Ising interactions. The quantum phase diagrams for ferro- and antiferromagnetic interactions on the chain and the square lattice are determined. The occurring superradiant phase transitions are in the same universality class as the Dicke model, leading to a well-known peculiar finite-size scaling that we elucidate in terms of scaling above the upper critical dimension. For the ferromagnetic case, the transition between the normal and the superradiant phase is of second order with Dicke criticality (first order) for large (small) longitudinal fields separated by a multicritical point. For antiferromagnetic interactions, we establish the light-matter analog of a lattice supersolid with off-diagonal superradiant and diagonal magnetic order and determine the nature of all transition lines. Our achievements allow to quantitatively enter the domain of mesoscopic light-matter systems, which is an increasingly prominent topic at the interface of quantum optics and condensed matter physics.
The dipole-coupled two-level atoms (qubits) in a single-mode resonant cavity are studied by extended bosonic coherent states. The numerical solution is presented. The first-order quantum phase transitions may occur in finite systems, in contrast to the original Dicke model. This system also exhibits a second-order quantum phase transition from the normal to the superradiant phase, as in the original Dicke model. Finite-size scaling for several observables---such as average fidelity susceptibility, order parameter, and concurrence---is performed for different interatomic interactions. The scaling exponents obtained suggest that interatomic interactions do not change the universality class.
The Dicke model is a fundamental model of quantum optics, which describes the interaction between light and matter. In the Dicke model, the light component is described as a single quantum mode, while the matter is described as a set of two-level systems. When the coupling between the light and matter crosses a critical value, the Dicke model shows a mean-field phase transition to a superradiant phase. This transition belongs to the Ising universality class and was realized experimentally in cavity quantum electrodynamics experiments. Although the superradiant transition bears some analogy with the lasing instability, these two transitions belong to different universality classes.
We study the entanglement near a quantum phase transition in a class of exactly solvable one‐dimensional quantum magnets, the anisotropic XY models. The critical behaviour (scaling) is reflected by the derivatives of the bipartite entanglent, quantified by the concurrence. However, we found a profound difference between classical correlation and non‐local quantum correlation: The range of the concurrence is found to behave in a non‐universal way, being extremely short‐ranged for the Ising model. This range tends to infinity towards the isotropic XY model.