Phase diagram of the quantum Ising model with long-range interactions on an infinite-cylinder triangular lattice

Abstract

Obtaining quantitative ground-state behavior for geometrically-frustrated quantum magnets with long-range interactions is challenging for numerical methods. Here, we demonstrate that the ground states of these systems on two-dimensional lattices can be efficiently obtained using state-of-the-art translation-invariant variants of matrix product states and density-matrix renormalization-group algorithms. We use these methods to calculate the fully-quantitative ground-state phase diagram of the long-range interacting triangular Ising model with a transverse field on 6-leg infinite-length cylinders, and scrutinize the properties of the detected phases. We compare these results with those of the corresponding nearest neighbor model. Our results suggest that, for such long-range Hamiltonians, the long-range quantum fluctuations always lead to long-range correlations, where correlators exhibit power-law decays instead of the conventional exponential drops observed for short-range correlated gapped phases. Our results are relevant for comparisons with recent ion-trap quantum simulator experiments that demonstrate highly-controllable long-range spin couplings for several hundred ions.

arXiv comment16 pages, 12 figures, and no supplemental materials. v4: equivalent to the published version, except a few minor typographical and notation corrections

References in corpus (55)

• The density-matrix renormalization group in the age of matrix product states
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• Exploring the many-body localization transition in two dimensions
• Quantum Orders and Symmetric Spin Liquids
• Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
• Many-body localization in a quantum simulator with programmable random disorder
• Time-dependent variational principle for quantum lattices
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Spin-lattice coupling in frustrated antiferromagnets
• Many-body localization: an introduction and selected topics
• Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
• Quantum spin dynamics and entanglement generation with hundreds of trapped ions
• From density-matrix renormalization group to matrix product states
• A class of ansatz wave functions for 1D spin systems and their relation to DMRG
• Ising models of quantum frustration
• Studying Two Dimensional Systems With the Density Matrix Renormalization Group
• Neel order in square and triangular lattice Heisenberg models
• Time-evolving a matrix product state with long-ranged interactions
• Can One Trust Quantum Simulators?
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Spin liquid phase of the $S=\frac{1}{2}$ $J_1-J_2$ Heisenberg model on the triangular lattice
• Emulating many-body localization with a superconducting quantum processor
• Entanglement entropy for the long range Ising chain
• Ground state entanglement and geometric entropy in the Kitaev's model
• Entanglement growth in quench dynamics with variable range interactions
• Competing Spin Liquid States in the Spin-$1/2$ Heisenberg Model On Triangular Lattice
• Two-dimensional periodic frustrated Ising models in a transverse field
• Applying matrix product operators to model systems with long-range interactions
• Long-range Ising and Kitaev Models: Phases, Correlations and Edge Modes
• The phase diagram of the hexagonal lattice quantum dimer model
• Generic Construction of Efficient Matrix Product Operators
• Anomalous dynamical phase in quantum spin chains with long-range interactions
• Interplay of quantum and thermal fluctuations in a frustrated magnet
• Continuous symmetry breaking and a new universality class in 1D long-range interacting quantum systems
• Many-Body Delocalization in Strongly Disordered System with Long-Range Interactions: Finite Size Scaling
• Anomalous Behavior of Spin Systems with Dipolar Interactions
• Infinite size density matrix renormalization group, revisited
• Ground states of a frustrated quantum spin chain with long-range interactions
• Kaleidoscope of quantum phases in a long-range interacting spin-1 chain
• Entanglement area laws for long-range interacting systems
• Frustrated quantum magnets
• Critical Phenomena and Kibble-Zurek Scaling in the Long-Range Quantum Ising Chain
• Critical behavior of quantum magnets with long-range interactions in the thermodynamic limit
• Topological phases with long-range interactions
• Quantum s = 1/2 Antiferromagnets on Archimedean Lattices: The Route from Semiclassical Magnetic Order to Nonmagnetic Quantum States
• $J_1-J_2$ quantum Heisenberg antiferromagnet on the triangular lattice: a group symmetry analysis of order by disorder
• Detection and characterization of symmetry-broken long-range orders in the spin-$\frac{1}{2}$ triangular Heisenberg model
• Disorder by disorder and flat bands in the kagome transverse field Ising model
• Quantum Monte Carlo Study of Long-Range Transverse-Field Ising Models on the Triangular Lattice
• Phase Diagram of the Spin-$1/2$ Triangular $J_1$-$J_2$ Heisenberg Model on a 3-leg Cylinder
• Schur Forms of Matrix Product Operators in the Infinite Limit
• Correlations and enlarged superconducting phase of $t$-$J_{\perp }$ chains of ultracold molecules on optical lattices

Cited by in corpus (18)

• Review on novel methods for lattice gauge theories
• Fidelity and criticality of quantum Ising chain with long-range interactions
• Quantum criticality of two-dimensional quantum magnets with long-range interactions
• Quantum-critical properties of the long-range transverse-field Ising model from quantum Monte Carlo simulations
• One-dimensional quantum many body systems with long-range interactions
• Quantum criticality and excitations of a long-range anisotropic $XY$-chain in a transverse field
• Dynamical structure factors of dynamical quantum simulators
• Quantum criticality of the transverse-field Ising model with long-range interactions on triangular-lattice cylinders
• Nonperturbative Waveguide Quantum Electrodynamics
• Scaling at quantum phase transitions above the upper critical dimension
• Hybrid infinite time-evolving block decimation algorithm for long-range multi-dimensional quantum many-body systems
• Monte Carlo based techniques for quantum magnets with long-range interactions
• Systematic Analysis of Crystalline Phases in Bosonic Lattice Models with Algebraically Decaying Density-Density Interactions
• Quantum phases of hardcore bosons with repulsive dipolar density-density interactions on two-dimensional lattices
• Exact Continuum Representation of Long-range Interacting Systems and Emerging Exotic Phases in Unconventional Superconductors
• Quantum Phase Transitions in Long-Range Interacting Hyperuniform Spin Chains in a Transverse Field
• Finding the ground states of symmetric infinite-dimensional Hamiltonians: explicit constrained optimizations of tensor networks
• Deconfined quantum criticality on a triangular Rydberg array