Density matrix renormalization group approach of the spin-boson model

Abstract

We propose a density matrix renormalization group approach to tackle a two-state system coupled to a bosonic bath with continuous spectrum. In this approach, the optimized phonon scheme is applied to several hundred phonon modes which are divided linearly among the spectrum. Although DMRG cannot resolve very small energy scales, the delocalized-localized transition points of the two-state system are extracted by the extrapolation of the flow diagram results. The phase diagram is compared with the numerical renormalization group results and shows good agreement in both Ohmic and sub-Ohmic cases.

6 pages, 7 figures

References in corpus (20)

• The density-matrix renormalization group
• The numerical renormalization group method for quantum impurity systems
• Quantum phase transitions
• Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic Spin-Boson Model
• Density matrix renormalization group algorithms with a single center site
• Spin Gaps in a Frustrated Heisenberg model for CaV${}_4$O${}_9$
• Numerical Renormalization Group for Quantum Impurities in a Bosonic Bath
• Equilibrium and non-equilibrium dynamics of the sub-ohmic spin-boson model
• Density Matrix Approach to Local Hilbert Space Reduction
• On the spin--boson model with a sub--Ohmic bath
• Entanglement and Criticality in Quantum Impurity Systems
• On the accuracy of the density matrix renormalization group method
• Quantum dynamics of the dissipative two-state system coupled with a sub-Ohmic bath
• Optimized phonon approach for the diagonalization of electron-phonon problems
• Coherent-incoherent transition in the sub-Ohmic spin-boson model
• Investigation of Quantum Phase Transitions using Multi-target DMRG Methods
• Hidden Caldeira-Leggett dissipation in a Bose-Fermi Kondo model
• Quantum Ising model in a transverse random field: A density-matrix renormalization group analysis
• Numerical analysis of the dissipative two-state system with the density-matrix Hilbert-space-reduction algorithm
• Antiferromagnetic integer-spin chains in a staggered magnetic field: approaching the thermodynamic limit through the infinite-size DMRG

Cited by in corpus (20)

• Critical and strong-coupling phases in one- and two-bath spin-boson models
• A generalized multi-polaron expansion for the spin-boson model: Environmental entanglement and the biased two-state system
• Quantum Phase Transition in the Sub-Ohmic Spin-Boson Model: Extended Coherent-state Approach
• Charge-density-wave melting in the one-dimensional Holstein model
• Finite-temperature density-matrix renormalization group method for electron-phonon systems: Thermodynamics and Holstein-polaron spectral functions
• Numerical Renormalization Group for the sub-ohmic spin-boson model: A conspiracy of errors
• Separation-dependent localization in a two-impurity spin-boson model
• Signatures of Dissipation Driven Quantum Phase Transition in Rabi Model
• Comparative Study of State-of-the-Art Matrix-Product-State Methods for Lattice Models with Large Local Hilbert Spaces
• Heat transport via a local two-state system near thermal equilibrium
• Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods
• Stable bipolarons in open quantum systems
• Improved Silbey-Harris polaron ansatz for the spin-boson model
• Transient dynamical phase diagram of the spin-boson model
• Artifact of the phonon-induced localization by variational calculations in the spin-boson model
• Qubit-oscillator relationships in the open quantum Rabi model: the role of dissipation
• Transient Dynamical Phase Diagram of the Spin-Boson Model at Finite Temperature
• Quantum criticality in sub-Ohmic systems with three competing terms: beyond conventional spin-boson physics
• Single Mode Approximation for sub-Ohmic Spin-Boson Model: Adiabatic Limit and Critical Properties
• No spin-localization phase transition in the spin-boson model without local field