Matrix product states and the nonabelian rotor model

Abstract

We use uniform matrix product states (MPS) to study the (1+1)D $O(2)$ and $O(4)$ rotor models, which are equivalent to the Kogut-Susskind formulation of matter-free nonabelian lattice gauge theory on a "hawaiian earring" graph for $U(1)$ and $SU(2)$, respectively. Applying tangent space methods to obtain ground states and determine the mass gap and the $\beta$ function, we find excellent agreement with known results, locating the BKT transition for $O(2)$ and successfully entering the asymptotic weak-coupling regime for $O(4)$. To obtain a finite local Hilbert space, we truncate in the space of generalized Fourier modes of the gauge group, comparing the effects of different cutoff values. We find that higher modes become important in the crossover and weak-coupling regimes of the nonabelian theory, where entanglement also suddenly increases. This could have important consequences for TNS studies of Yang-Mills on higher dimensional graphs.

6 pages, 4 figures. Code at https://github.com/amilsted/mps-rotors

References in corpus (12)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Ab-initio Determination of Light Hadron Masses
• Tensor renormalization group approach to 2D classical lattice models
• Scaling of entanglement support for Matrix Product States
• Gauging quantum states: from global to local symmetries in many-body systems
• Tensor Networks for Lattice Gauge Theories with continuous groups
• Grassmann Tensor Renormalization Group Approach to One-Flavor Lattice Schwinger Model
• Non-Abelian string breaking phenomena with Matrix Product States
• Entanglement renormalization and gauge symmetry
• Lattice Gauge Tensor Networks
• Transfer Matrices and Excitations with Matrix Product States

Cited by in corpus (18)

• Review on novel methods for lattice gauge theories
• Efficient Basis Formulation for (1+1)-Dimensional SU(2) Lattice Gauge Theory: Spectral calculations with matrix product states
• Real-time simulation of the Schwinger effect with Matrix Product States
• Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks
• 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
• Projected Entangled Pair States with non-Abelian gauge symmetries: an SU(2) study
• O(3) nonlinear sigma model in 1+1 dimensions with matrix product states
• Combining Tensor Networks with Monte Carlo Methods for Lattice Gauge Theories
• Classification of Matrix Product States with a Local (Gauge) Symmetry
• Truncation effects in the charge representation of the O(2) model
• Quantum Yang-Mills theory: an overview of a programme
• Gauss Law, Minimal Coupling and Fermionic PEPS for Lattice Gauge Theories
• Tensor network simulation of the (1+1)-dimensional $O(3)$ nonlinear $\sigma$-model with $\theta =\pi$ term
• Entanglement renormalization for gauge invariant quantum fields
• Lattice regularisation and entanglement structure of the Gross-Neveu model
• Spin chains, defects, and quantum wires for the quantum-double edge