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

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.

arXiv comment13 pages, 9 figures, version 2: slightly different title, published version

References in corpus (55)

• The density-matrix renormalization group in the age of matrix product states
• Entanglement Entropy and Quantum Field Theory
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• An Area Law for One Dimensional Quantum Systems
• Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
• DMRG and periodic boundary conditions: a quantum information perspective
• Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
• Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model
• The mass spectrum of the Schwinger model with Matrix Product States
• Functional integrals for QCD at nonzero chemical potential and zero density
• Tensor networks for Lattice Gauge Theories and Atomic Quantum Simulation
• Density Matrix Renormalisation Group Approach to the Massive Schwinger Model
• U(1) Wilson lattice gauge theories in digital quantum simulators
• Matrix product states for gauge field theories
• Instantons in the Higgs Phase
• Real-time Dynamics in U(1) Lattice Gauge Theories with Tensor Networks
• Continuity and Resurgence: towards a continuum definition of the CP(N-1) model
• Resurgence in QFT: Unitons, Fractons and Renormalons in the Principal Chiral Model
• Quantum simulation of the Schwinger model: A study of feasibility
• Grassmann Tensor Renormalization Group Approach to One-Flavor Lattice Schwinger Model
• Non-Abelian string breaking phenomena with Matrix Product States
• Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States
• Non-Abelian Vortices on Cylinder -- Duality between vortices and walls
• Efficient Basis Formulation for (1+1)-Dimensional SU(2) Lattice Gauge Theory: Spectral calculations with matrix product states
• Lattice Gauge Tensor Networks
• Thermal evolution of the Schwinger model with Matrix Product Operators
• Real-time simulation of the Schwinger effect with Matrix Product States
• Chiral condensate in the Schwinger model with Matrix Product Operators
• Hamiltonian simulation of the Schwinger model at finite temperature
• Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks
• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• Finite-density phase diagram of a (1+1)-d non-abelian lattice gauge theory with tensor networks
• Variational study of U(1) and SU(2) lattice gauge theories with Gaussian states in 1+1 dimensions
• Confinement and string breaking for QED${}_2$ in the Hamiltonian picture
• Instanton constituents in the O(3) model at finite temperature
• Finite size effects in the presence of a chemical potential: A study in the classical non-linear O(2) sigma-model
• Instanton constituents and fermionic zero modes in twisted CP(n) models
• Tensor renormalization group analysis of CP(N-1) model
• Density matrix renormalization group in a two-dimensional $\lambda {\varphi }^4$ Hamiltonian lattice model
• Dual lattice representations for O(N) and CP(N-1) models with a chemical potential
• Progress towards quantum simulating the classical O(2) model
• The fine structure of the entanglement entropy in the classical XY model
• Tensor network simulation of QED on infinite lattices: learning from (1+1)d, and prospects for (2+1)d
• Towards overcoming the Monte Carlo sign problem with tensor networks
• Kinks, chains, and loop groups in the CP^n sigma models
• Matrix product states and the nonabelian rotor model
• The two-dimensional O(3) model at nonzero density: from dual lattice simulations to repulsive bosons
• Probing the conformal Calabrese-Cardy scaling with cold atoms
• Estimating the central charge from the Rényi entanglement entropy
• Nonlinear sigma models at nonzero chemical potential: breaking up instantons and the phase diagram
• Grand canonical ensemble, multi-particle wave functions, scattering data, and lattice field theories
• Thermal evolution of the one-flavour Schwinger model using Matrix Product States
• Complex instantons in sigma models with chemical potential
• Gaussian states for the variational study of (1+1)-dimensional lattice gauge models

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• From asymptotic freedom to $\theta$ vacua: Qubit embeddings of the O(3) nonlinear $\sigma$ model
• Truncation effects in the charge representation of the O(2) model
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• Qubitization strategies for bosonic field theories
• Phase structure of the CP(1) model in the presence of a topological $\theta$-term
• Fuzzy gauge theory for quantum computers
• State Preparation in the Heisenberg Model through Adiabatic Spiraling
• Phase structure of the 1+1 dimensional massive Thirring model from matrix product states
• Preparation for Quantum Simulation of the 1+1D O(3) Non-linear σ-Model using Cold Atoms
• A variational Monte Carlo algorithm for lattice gauge theories with continuous gauge groups: a study of (2+1)-dimensional compact QED with dynamical fermions at finite density
• Universality of a truncated sigma-model
• Towards a Quantum Simulation of Nonlinear Sigma Models with a Topological Term
• Continuous variable quantum computation of the $O(3)$ model in 1+1 dimensions
• Topological susceptibility of $2d{\mathrm{CP}}^1$ or $\mathrm{O}(3)$ non-linear $\sigma$-model: is it divergent or not?
• Real-Time Scattering in Ising Field Theory using Matrix Product States
• Tensor network simulation of the (1+1)-dimensional $O(3)$ nonlinear $\sigma$-model with $\theta =\pi$ term
• Lattice regularizations of $\theta$ vacua: Anomalies and qubit models
• Entanglement renormalization for gauge invariant quantum fields
• Toward quantum computations of the $O(3)$ model using qumodes
• Lattice regularisation and entanglement structure of the Gross-Neveu model