Phase structure of the one-dimensional ${\mathbb{Z}}_2$ lattice gauge theory with second nearest-neighbor interactions

Abstract

We investigate the ground-state phase diagram of a one-dimensional ${\mathbb{Z}}_2$ lattice gauge theory (LGT) model with hard-core bosons at half-filling, extending previous studies by including second nearest-neighbor (2NN) interactions. Using matrix product state techniques within the density matrix renormalization group, we compute charge gap, static structure factor, pair-pair correlation functions, and entanglement entropy for various interaction strengths and field parameters. We analyze two representative neatest-neighbor interaction strengths ($V_1$) that correspond to the Luttinger liquid (LL) and Mott insulator (MI) phases in the absence of the 2NN interactions. We introduce the 2NN coupling $V_2$ and investigate its impact on the system. Our results reveal very rich behavior. As the 2NN repulsion increases, in the case of small $V_1$, we observe a direct transition from the LL phase to a charge-ordered insulator (COI) phase with four-site ordering pattern, whereas for large $V_1$, we observe a transition from the MI phase with two-site ordering pattern (previously found with only $V_1$ included), going through an intermediate LL region, and finally reaching the COI regime. Additionally, the inclusion of 2NN interactions enhances charge order and suppresses pair coherence, evidenced by sharp peaks in the structure factor and rapid decay in pair-pair correlators. Our work extends the well-studied phase structure of 1D ${\mathbb{Z}}_2$ LGT models and demonstrates the interplay between gauge fields, confinement, and extended interactions.

arXiv comment14 pages, 13 figures (including 30 panels), 63 references; RevTeX class, double-column formatting; BKT discussion with 1 figure and 10 references added with respect to previous version, minor typos corrected. This is the author created version of an article submitted to and accepted/published in Physical Review B journal

References in corpus (45)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Entanglement Entropy and Quantum Field Theory
• Probing many-body dynamics on a 51-atom quantum simulator
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Quantum Spin Liquids
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Efficient simulation of one-dimensional quantum many-body systems
• Entanglement entropy and conformal field theory
• String-net condensation: A physical mechanism for topological phases
• Entanglement renormalization
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems
• DMRG and periodic boundary conditions: a quantum information perspective
• Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
• Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories
• Floquet approach to ${\mathbb{Z}}_2$ lattice gauge theories with ultracold atoms in optical lattices
• Matrix product operator representations
• Long-range interacting quantum systems
• Lattice gauge theories and string dynamics in Rydberg atom quantum simulators
• Lattice gauge theories simulations in the quantum information era
• Lattice QCD at non-zero temperature
• Simulating 2+1d Lattice QED with dynamical matter using ultracold atoms
• Superconducting Circuits for Quantum Simulation of Dynamical Gauge Fields
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• Tensor Network Algorithms: a Route Map
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Confined phases of one-dimensional spinless fermions coupled to $Z_2$ gauge theory
• Quantum-gas microscopes - A new tool for cold-atom quantum simulators
• Simple ${\mathbb{Z}}_2$ lattice gauge theories at finite fermion density
• From Quantum Link Models to D-Theory: A Resource Efficient Framework for the Quantum Simulation and Computation of Gauge Theories
• Doping driven metal-insulator transitions and charge orderings in the extended Hubbard model
• Three-dimensional finite temperature Z${}_2$ gauge theory with tensor network scheme
• Phenomenological Z_2 lattice gauge theory of the spin-liquid state of the kagome Heisenberg antiferromagnet
• Lattice Gauge Theory for Condensed Matter Physics: Ferromagnetic Superconductivity as its Example
• Phase structure of the 1+1 dimensional massive Thirring model from matrix product states
• Extended Falicov-Kimball model: Exact solution for finite temperatures
• Transverse force distributions in the proton from lattice QCD
• Extended Falicov-Kimball model: exact solution for the ground state
• Confinement Induced Frustration in a One-Dimensional ${\mathbb{Z}}_2$ Lattice Gauge Theory
• Quantum Simulation of non-Abelian Lattice Gauge Theories: a variational approach to ${\mathbb{D}}_8$
• Dynamics of a Lattice Gauge Theory with Fermionic Matter -- Minimal Quantum Simulator with Time-Dependent Impurities in Ultracold Gases
• Particle-Hole Asymmetry and Pinball Liquid in a Triangular-Lattice Extended Hubbard Model within Mean-Field Approximation