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:1812.00944 · Physical review. D/Physical review. D.

O(3) nonlinear sigma model in 1+1 dimensions with matrix product states

Falk Bruckmann A, Karl Jansen, Stefan Kühn

Published Apr 1, 2019• 41 citations
arXivHTMLPDF

Abstract

We numerically study the spectral properties, the entanglement and the zero-temperature phase structure at nonvanishing chemical potential of the O(3) nonlinear sigma model. Using matrix product states, a particular kind of one-dimensional tensor network state, we show that we are able to reach the asymptotic scaling regime and to reproduce the analytical predictions for the mass gap at vanishing chemical potential. In addition, we study the scaling of the entanglement entropy towards the continuum limit obtaining a central charge consistent with 2. Moreover, our approach does not suffer from the sign problem and we also explore the phase structure of the model for nonzero chemical potential and map out the location of the transitions between different charge sectors with high precision.

DOI
10.1103/physrevd.99.074501

Related papers

Tensor renormalization group study of (1+1)-dimensional O(3) nonlinear sigma model with and without finite chemical potential

Xiao Luo, Y. Kuramashi

We study (1+1)-dimensional O(3) nonlinear sigma model using the tensor renormalization group method with the infinite limit of the bond dimension $D_{\rm cut}\rightarrow \infty$. At the vanishing chemical potential $μ=0$, we investigate the von Neumann and Rényi types of entanglement entropies. The central charge is determined to be $c=1.97(9)$ by using the asymptotic scaling properties of the entropies. We also examine the consistency between two entropies. In the finite density region with $μ\ne 0$, where this model suffers from the sign problem in the standard Monte Carlo approach, we investigate the properties of the quantum phase transition. We determine the transition point $μ_{\rm c}$ and the critical exponent of the correlation length $ν$ from the $μ$ dependence of the number density in the thermodynamic limit. The dynamical critical exponent $z$ is also extracted from the scaling behavior of the temporal correlation length as a function of $μ$. This is the first successful calculation of the dynamical critical exponent with the TRG method.

arXiv:2412.02995•Dec 4, 2024•0 citations

Tensor renormalization group study of (1+1)-dimensional O(3) nonlinear sigma model with and without finite chemical potential

Y. Kuramashi, Xiao Luo

We study (1+1)-dimensional O(3) nonlinear sigma model using the tensor renormalization group method with the infinite limit of the bond dimension $D_{\rm cut}\rightarrow \infty$. At the vanishing chemical potential $\mu=0$, we investigate the von Neumann and R\'enyi types of entanglement entropies. The central charge is determined to be $c=1.97(9)$ by using the asymptotic scaling properties of the entropies. We also examine the consistency between two entropies. In the finite density region with $\mu\ne 0$, where this model suffers from the sign problem in the standard Monte Carlo approach, we investigate the properties of the quantum phase transition. We determine the transition point $\mu_{\rm c}$ and the critical exponent of the correlation length $\nu$ from the $\mu$ dependence of the number density in the thermodynamic limit. The dynamical critical exponent $z$ is also extracted from the scaling behavior of the temporal correlation length as a function of $\mu$. This is the first successful calculation of the dynamical critical exponent with the TRG method.

International Symposium on Lattice Field Theory (LATTICE)•Dec 5, 2024•0 citations

Two-dimensional O(3) model at nonzero density: From dual lattice simulations to repulsive bosons

Falk Bruckmann A, Christof Gattringer, Thomas Kloiber +1 more

We discuss the thermodynamics of the O(3) nonlinear sigma model in $1+1$ dimensions at nonzero chemical potential (equivalent to a magnetic field). In its conventional field theory representation the model suffers from a sign problem. By dualizing the model, we are able to fully access the nonzero density regime of an asymptotically free theory with dynamical mass gap at arbitrary chemical potential values. We find a quantum phase transition at zero temperature where as a function of the chemical potential the density assumes a nonzero value. Measuring the spin stiffness we present evidence for a corresponding dynamical critical exponent $z$ close to 2. The low energy O(3) model is conjectured to be described by a massive boson triplet with repulsive interactions. We confirm the universal square-root behavior expected for such a system at low density (and temperature) and compare our data to the results of Bethe Ansatz solutions of the relativistic and nonrelativistic one-dimensional Bose gas. We also comment on a potential Berezinskii-Kosterlitz-Thouless transition at nonzero density.

arXiv:1607.02457•Physical review. D/Physical review. D.•Dec 2, 2016•22 citations

Quantum phase transition of (1+1)-dimensional O(3) nonlinear sigma model at finite density with tensor renormalization group

Luo Xiao, Kuramashi Yoshinobu

We study the quantum phase transition of the (1+1)-dimensional O(3) nonlinear sigma model at finite density using the tensor renormalization group method. This model suffers from the sign problem, which has prevented us from investigating the properties of the phase transition. We investigate the properties of the phase transition by changing the chemical potential mu at a fixed coupling of beta. We determine the transition point mu c and the critical exponent nu from the mu dependence of the number density in the thermodynamic limit. The dynamical critical exponent z is also extracted from the scaling behavior of the temporal correlation length as a function of mu.

•Nov 26, 2024•0 citations

Quantum phase transition of (1+1)-dimensional O(3) nonlinear sigma model at finite density with tensor renormalization group

Xiao Luo, Y. Kuramashi

A bstract We study the quantum phase transition of the (1+1)-dimensional O(3) nonlinear sigma model at finite density using the tensor renormalization group method. This model suffers from the sign problem, which has prevented us from investigating the properties of the phase transition. We investigate the properties of the phase transition by changing the chemical potential μ at a fixed coupling of β . We determine the transition point μ c and the critical exponent ν from the μ dependence of the number density in the thermodynamic limit. The dynamical critical exponent z is also extracted from the scaling behavior of the temporal correlation length as a function of μ .

arXiv:2406.08865•Journal of High Energy Physics•Nov 26, 2024•1 citation

Entanglement and Rényi entropies of (1+1)-dimensional O(3) nonlinear sigma model with tensor renormalization group

Xiao Luo, Y. Kuramashi

A bstract We investigate the entanglement and Rényi entropies for the (1+1)-dimensional O(3) nonlinear sigma model using the tensor renormalization group method. The central charge is determined from the asymptotic scaling properties of both entropies. We also examine the consistency between the entanglement entropy and the n th-order Rényi entropy with n → 1.

arXiv:2308.02798•Journal of High Energy Physics•Mar 4, 2024•4 citations
We numerically study the spectral properties, the entanglement and the zero-temperature phase structure at nonvanishing chemical potential of the O(3) nonlinear sigma model. Using matrix product states, a particular kind of one-dimensional tensor network state, we show that we are able to reach the asymptotic scaling regime and to reproduce the analytical predictions for the mass gap at vanishing chemical potential. In addition, we study the scaling of the entanglement entropy towards the continuum limit obtaining a central charge consistent with 2. Moreover, our approach does not suffer from the sign problem and we also explore the phase structure of the model for nonzero chemical potential and map out the location of the transitions between different charge sectors with high precision.
We study (1+1)-dimensional O(3) nonlinear sigma model using the tensor renormalization group method with the infinite limit of the bond dimension Dcut→∞D_{\rm cut}\rightarrow \inftyDcut​→∞. At the vanishing chemical potential μ=0μ=0μ=0, we investigate the von Neumann and Rényi types of entanglement entropies. The central charge is determined to be c=1.97(9)c=1.97(9)c=1.97(9) by using the asymptotic scaling properties of the entropies. We also examine the consistency between two entropies. In the finite density region with μ≠0μ\ne 0μ=0, where this model suffers from the sign problem in the standard Monte Carlo approach, we investigate the properties of the quantum phase transition. We determine the transition point μcμ_{\rm c}μc​ and the critical exponent of the correlation length ννν from the μμμ dependence of the number density in the thermodynamic limit. The dynamical critical exponent zzz is also extracted from the scaling behavior of the temporal correlation length as a function of μμμ. This is the first successful calculation of the dynamical critical exponent with the TRG method.
We study (1+1)-dimensional O(3) nonlinear sigma model using the tensor renormalization group method with the infinite limit of the bond dimension Dcut→∞D_{\rm cut}\rightarrow \inftyDcut​→∞. At the vanishing chemical potential μ=0\mu=0μ=0, we investigate the von Neumann and R\'enyi types of entanglement entropies. The central charge is determined to be c=1.97(9)c=1.97(9)c=1.97(9) by using the asymptotic scaling properties of the entropies. We also examine the consistency between two entropies. In the finite density region with μ≠0\mu\ne 0μ=0, where this model suffers from the sign problem in the standard Monte Carlo approach, we investigate the properties of the quantum phase transition. We determine the transition point μc\mu_{\rm c}μc​ and the critical exponent of the correlation length ν\nuν from the μ\muμ dependence of the number density in the thermodynamic limit. The dynamical critical exponent zzz is also extracted from the scaling behavior of the temporal correlation length as a function of μ\muμ. This is the first successful calculation of the dynamical critical exponent with the TRG method.
We discuss the thermodynamics of the O(3) nonlinear sigma model in 1+11+11+1 dimensions at nonzero chemical potential (equivalent to a magnetic field). In its conventional field theory representation the model suffers from a sign problem. By dualizing the model, we are able to fully access the nonzero density regime of an asymptotically free theory with dynamical mass gap at arbitrary chemical potential values. We find a quantum phase transition at zero temperature where as a function of the chemical potential the density assumes a nonzero value. Measuring the spin stiffness we present evidence for a corresponding dynamical critical exponent zzz close to 2. The low energy O(3) model is conjectured to be described by a massive boson triplet with repulsive interactions. We confirm the universal square-root behavior expected for such a system at low density (and temperature) and compare our data to the results of Bethe Ansatz solutions of the relativistic and nonrelativistic one-dimensional Bose gas. We also comment on a potential Berezinskii-Kosterlitz-Thouless transition at nonzero density.
We study the quantum phase transition of the (1+1)-dimensional O(3) nonlinear sigma model at finite density using the tensor renormalization group method. This model suffers from the sign problem, which has prevented us from investigating the properties of the phase transition. We investigate the properties of the phase transition by changing the chemical potential mu at a fixed coupling of beta. We determine the transition point mu c and the critical exponent nu from the mu dependence of the number density in the thermodynamic limit. The dynamical critical exponent z is also extracted from the scaling behavior of the temporal correlation length as a function of mu.
A bstract We study the quantum phase transition of the (1+1)-dimensional O(3) nonlinear sigma model at finite density using the tensor renormalization group method. This model suffers from the sign problem, which has prevented us from investigating the properties of the phase transition. We investigate the properties of the phase transition by changing the chemical potential μ at a fixed coupling of β . We determine the transition point μ c and the critical exponent ν from the μ dependence of the number density in the thermodynamic limit. The dynamical critical exponent z is also extracted from the scaling behavior of the temporal correlation length as a function of μ .