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:1312.1958 · Physica Scripta

Efficient basis for the Dicke model: II. Wave function convergence and excited states

Jorge G Hirsch, M. A. Bastarrachea-Magnani

Published Apr 1, 2014• 20 citations
arXivHTMLPDF

Abstract

An extended bosonic coherent basis has been shown by Chen et al to provide numerically exact solutions of the finite-size Dicke model. The advantages in employing this basis, as compared with the photon number (Fock) basis, are exhibited to be valid for a large region of the Hamiltonian parameter space and many excited states by analyzing the convergence in the wave functions.

DOI
10.1088/0031-8949/2014/t160/014018

Related papers

Efficient basis for the Dicke model: I. Theory and convergence in energy

M. A. Bastarrachea-Magnani, Jorge G Hirsch

An extended bosonic coherent basis has been shown by Chen et al (2008 Phys. Rev. A 78 051801) and Liu et al (2009 Phys. Rev. A 80 165308) to provide numerically exact solutions of the finite-size Dicke model. The advantages in employing this basis, as compared with the photon number (Fock) basis, are exhibited to be valid for a large region of the Hamiltonian parameter space by analyzing the converged values of the ground state energy.

arXiv:1312.1954•Physica Scripta•Apr 1, 2014•22 citations

Numerical solutions of the Dicke Hamiltonian

M. A. Bastarrachea-Magnani, Jorge G. Hirsch

We study the numerical solutions of the Dicke Hamiltonian, which describes a system of many two level atoms interacting with a monochromatic radiation field into a cavity. The Dicke model is an example of a quantum collective behavior which shows superradiant quantum phase transitions in the thermodynamic limit. Results obtained employing two different bases are compared. Both of them use the pseudospin basis to describe the atomic states. For the photon states we use in one case Fock states, while in the other case we use a basis built over a particular coherent state, associated to each atomic state. It is shown that, when the number of atoms increases, the description of the ground state of the system in the superradiant phase requires an equivalent number of photons to be included. This imposes a strong limit to the states that can be calculated using Fock states, while the dimensionality needed to obtain convergent results in the other basis decreases when the atomic number increases, allowing calculations that are very difficult in the Fock basis. Naturally, it reduces also the computing time, economizing computing resources. We show results for the energy, the photon number and the number of excited atoms, for the ground and the first excited state.

arXiv:1108.0703•Revista Mexicana de Física•Aug 2, 2011•11 citations

Numerically exact solution to the finite-size Dicke model

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

By using extended bosonic coherent states, a technique to solve the Dicke model exactly is proposed in the numerical sense. The accessible system size is two orders of magnitude higher than that reported in the literature. Finite-size scaling for several observables, such as the ground-state energy, Berry phase, and concurrence, is analyzed. A scaling exponent for ground-state energy is found. An existing discrepancy in the scaling exponent of the concurrence is reconciled.

arXiv:0809.4385•Physical Review A•Nov 3, 2008•156 citations

Universal critical behavior in the Dicke model

Octavio Castaños, Eduardo Nahmad-Achar, Ramón López–Peña +1 more

The critical value of the atom-field coupling strength for a finite number of atoms is determined by means of both semiclassical and exact solutions. In the semiclassical approach we use a variational procedure with coherent and symmetry-adapted states, while for the exact quantum solution the concept of fidelity is employed. These procedures allow for the determination of the phase transitions in the model and coincide in the thermodynamic limit. For the three cases mentioned above, universal parametric curves are obtained for the expectation values of both the first quadrature of the electromagnetic field and the atomic relative population as implicit functions of the atom-field coupling parameter, valid for the ground and first-excited states.

arXiv:1206.0797•Physical Review A•Aug 8, 2012•25 citations

Universal critical behaviour in finite atom-field systems

Eduardo Nahmad-Achar, Octavio Castaños, Ramón López–Peña +1 more

The critical value of the atom-field coupling strength in the Dicke model, for a finite number of atoms interacting with photons in a cavity, is determined by means of semiclassical (via coherent states and symmetry-adapted states) and exact solutions. These procedures allow in turn for the determination of the phase transitions in the model, and coincide in the thermodynamic limit. For the three cases mentioned above, a universal parametric curve is obtained for the expectation values of the first quadrature of the electromagnetic field, as a function of the atomic relative population, valid for all values of the atom-field coupling parameter, and valid for the ground-and first-excited states.

AIP conference proceedings•Jan 1, 2012•0 citations

Chaos and Thermalization in the Spin-Boson Dicke Model

David Villaseñor, Saúl Pilatowsky-Cameo, M. A. Bastarrachea-Magnani +3 more

We present a detailed analysis of the connection between chaos and the onset of thermalization in the spin-boson Dicke model. This system has a well-defined classical limit with two degrees of freedom, and it presents both regular and chaotic regions. Our studies of the eigenstate expectation values and the distributions of the off-diagonal elements of the number of photons and the number of excited atoms validate the diagonal and off-diagonal eigenstate thermalization hypothesis (ETH) in the chaotic region, thus ensuring thermalization. The validity of the ETH reflects the chaotic structure of the eigenstates, which we corroborate using the von Neumann entanglement entropy and the Shannon entropy. Our results for the Shannon entropy also make evident the advantages of the so-called "efficient basis" over the widespread employed Fock basis when investigating the unbounded spectrum of the Dicke model. The efficient basis gives us access to a larger number of converged states than what can be reached with the Fock basis.

arXiv:2211.08434•Entropy•Dec 21, 2022•24 citations
An extended bosonic coherent basis has been shown by Chen et al to provide numerically exact solutions of the finite-size Dicke model. The advantages in employing this basis, as compared with the photon number (Fock) basis, are exhibited to be valid for a large region of the Hamiltonian parameter space and many excited states by analyzing the convergence in the wave functions.
We study the numerical solutions of the Dicke Hamiltonian, which describes a system of many two level atoms interacting with a monochromatic radiation field into a cavity. The Dicke model is an example of a quantum collective behavior which shows superradiant quantum phase transitions in the thermodynamic limit. Results obtained employing two different bases are compared. Both of them use the pseudospin basis to describe the atomic states. For the photon states we use in one case Fock states, while in the other case we use a basis built over a particular coherent state, associated to each atomic state. It is shown that, when the number of atoms increases, the description of the ground state of the system in the superradiant phase requires an equivalent number of photons to be included. This imposes a strong limit to the states that can be calculated using Fock states, while the dimensionality needed to obtain convergent results in the other basis decreases when the atomic number increases, allowing calculations that are very difficult in the Fock basis. Naturally, it reduces also the computing time, economizing computing resources. We show results for the energy, the photon number and the number of excited atoms, for the ground and the first excited state.
The critical value of the atom-field coupling strength for a finite number of atoms is determined by means of both semiclassical and exact solutions. In the semiclassical approach we use a variational procedure with coherent and symmetry-adapted states, while for the exact quantum solution the concept of fidelity is employed. These procedures allow for the determination of the phase transitions in the model and coincide in the thermodynamic limit. For the three cases mentioned above, universal parametric curves are obtained for the expectation values of both the first quadrature of the electromagnetic field and the atomic relative population as implicit functions of the atom-field coupling parameter, valid for the ground and first-excited states.
The critical value of the atom-field coupling strength in the Dicke model, for a finite number of atoms interacting with photons in a cavity, is determined by means of semiclassical (via coherent states and symmetry-adapted states) and exact solutions. These procedures allow in turn for the determination of the phase transitions in the model, and coincide in the thermodynamic limit. For the three cases mentioned above, a universal parametric curve is obtained for the expectation values of the first quadrature of the electromagnetic field, as a function of the atomic relative population, valid for all values of the atom-field coupling parameter, and valid for the ground-and first-excited states.
We present a detailed analysis of the connection between chaos and the onset of thermalization in the spin-boson Dicke model. This system has a well-defined classical limit with two degrees of freedom, and it presents both regular and chaotic regions. Our studies of the eigenstate expectation values and the distributions of the off-diagonal elements of the number of photons and the number of excited atoms validate the diagonal and off-diagonal eigenstate thermalization hypothesis (ETH) in the chaotic region, thus ensuring thermalization. The validity of the ETH reflects the chaotic structure of the eigenstates, which we corroborate using the von Neumann entanglement entropy and the Shannon entropy. Our results for the Shannon entropy also make evident the advantages of the so-called "efficient basis" over the widespread employed Fock basis when investigating the unbounded spectrum of the Dicke model. The efficient basis gives us access to a larger number of converged states than what can be reached with the Fock basis.