Monte Carlo simulations of dissipative quantum Ising models

Abstract

The dynamical critical exponent $z$ is a fundamental quantity in characterizing quantum criticality, and it is well known that the presence of dissipation in a quantum model has significant impact on the value of $z$. Studying quantum Ising spin models using Monte Carlo methods, we estimate the dynamical critical exponent $z$ and the correlation length exponent $\nu$ for different forms of dissipation. For a two-dimensional quantum Ising model with Ohmic site dissipation, we find $z\approx 2$ as for the corresponding one-dimensional case, whereas for a one-dimensional quantum Ising model with Ohmic bond dissipation we obtain the estimate $z\approx 1$.

9 pages, 8 figures. Submitted to Physical Review B

References in corpus (19)

• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• Continuous Quantum Phase Transitions
• Quantum phase transitions
• High-precision finite-size scaling analysis of the quantum-critical point of S=1/2 Heisenberg antiferromagnetic bilayers
• Zero--Temperature Quantum Phase Transition of a Two--Dimensional Ising Spin--Glass
• Phase diagram and critical exponents of a dissipative Ising spin chain in a transverse magnetic field
• Criticality in one dimension with inverse square-law potentials
• Domain-Wall Free-Energy of Spin Glass Models:Numerical Method and Boundary Conditions
• Theory of the Quantum Critical Fluctuations in Cuprates
• Universal conductance of nanowires near the superconductor-metal quantum transition
• Non-Fermi liquid behavior from two-dimensional antiferromagnetic fluctuations: a renormalization-group and large-N analysis
• Quantum spin chains with site dissipation
• Quantum-Criticality in Dissipative Quantum Two-Dimensional XY and Ashkin-Teller Models: Application to the Cuprates
• Dissipation, topology, and quantum phase transition in a one-dimensional Joesphson junction array
• Floating phase in a dissipative Josephson junction array
• Cluster Monte Carlo Algorithms for Dissipative Quantum Systems
• Static properties of the dissipative random quantum Ising ferromagnetic chain
• Effective theory of fluctuating circulating currents in high-Tc cuprates
• Dissipate locally, couple globally: a sharp transition from decoupling to infinite range coupling in Josephson arrays with on-site dissipation

Cited by in corpus (14)

• Antiferromagnetic phase transition in a nonequilibrium lattice of Rydberg atoms
• Dynamical phases and intermittency of the dissipative quantum Ising model
• Nonequilibrium quantum criticality in open systems: The dissipation rate as an additional indispensable scaling variable
• Quantum criticality in spin chains with non-ohmic dissipation
• Decoherence in the quantum Ising model with transverse dissipative interaction in the strong coupling regime
• First-order transitions in spin chains coupled to quantum baths
• Critical properties of dissipative quantum spin systems in finite dimensions
• Dyson hierarchical quantum ferromagnetic Ising chain with pure or random transverse fields
• Quantum criticality in a dissipative (2+1)-dimensional XY model of circulating currents in high-Tc cuprates
• Criticality of compact and noncompact quantum dissipative $Z_4$ models in $(1+1)$ dimensions
• Properties of the simplest inhomogeneous and homogeneous Tree-Tensor-States for Long-Ranged Quantum Spin Chains with or without disorder
• Long-Range Order and Quantum Criticality in a Dissipative Spin Chain
• Stochastic parameter optimization analysis of dynamical quantum critical phenomena in long-range transverse-field Ising chain
• Singular transport in non-equilibrium strongly internal-coupled 1D tilted field spin-1/2 chain