Variational study of two-impurity spin-boson model with a common Ohmic bath: Ground-state phase transitions

Abstract

By means of a trial wave function, the multi-D${}_1$ ansatz, extensive variational calculations with more than ten thousand parameters have been carried out to study quantum phase transitions in the ground states of a two-impurity system embedded in a common Ohmic bath of bosons. Quantum criticality in both the impurity system and the Ohmic bosonic bath is investigated with relevant transition points and critical exponents determined accurately. With the linear grid of the Ohmic spectral density, our numerical calculations produce a much better description of the ground states with lower energies than other calculations employing a logarithmic grid with a discretization factor far greater than unity. It offers a possible solution to the considerable controversy on the critical coupling in the literature. Moreover, the ground-state phase transition is inferred to be of first order in the presence of strong antiferromagnetic spin-spin couplin}, at variance with that in the ferromagnetic regime or in the absence of spin-spin coupling where the transition belongs to the Kosterlitz-Thouless universality class.

13 pages, 10 figures

References in corpus (39)

• Dephasing in Quantum Dots: Quadratic Coupling to Acoustic Phonons
• Numerical Renormalization Group for Quantum Impurities in a Bosonic Bath
• Quantum phase transitions in the sub-ohmic spin-boson model: Failure of the quantum-classical mapping
• The quantum phase transition in the sub-ohmic spin-boson model: Quantum Monte-Carlo study with a continuous imaginary time cluster algorithm
• Spontaneous two photon emission from a single quantum dot
• Entanglement Entropy, decoherence, and quantum phase transition of a dissipative two-level system
• Critical and strong-coupling phases in one- and two-bath spin-boson models
• A variational description of the quantum phase transition in the sub-Ohmic spin-boson model
• Nonequilibrium and nonperturbative dynamics of ultrastrong coupling in open lines
• Dynamics, Synchronization and Quantum Phase Transitions of Two Dissipative Spins
• Sparse polynomial space approach to dissipative quantum systems: Application to the sub-ohmic spin-boson model
• Two-photon lasing by a single quantum dot in a high-Q microcavity
• Superradiant phase transition in the ultrastrong coupling regime of the two-photon Dicke model
• Inelastic Microwave Photon Scattering off a Quantum Impurity in a Josephson-Junction Array
• 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
• Universal Jump in the Helicity Modulus of the Two-Dimensional Quantum XY Model
• Kondo effect of impurity moments in d-wave superconductors: Quantum phase transition and spectral properties
• Variational dynamics of the sub-Ohmic spin-boson model on the basis of multiple Davydov ${\mathrm{D}}_1$ states
• Polaron dynamics with a multitude of Davydov D${}_2$ trial states
• Finite-temperature time-dependent variation with multiple Davydov states
• Simulating generic spin-boson models with matrix product states
• Nonequilibrium dynamics of spin-boson models from phase space methods
• Ground state and dynamics of the biased dissipative two-state system: Beyond variational polaron theory
• Dynamics of dissipative Landau-Zener transitions
• Separation-dependent localization in a two-impurity spin-boson model
• Nonequilibrium spin-boson model: from weak to strong coupling
• Two-bath spin-boson model: Phase diagram and critical properties
• Anatomy of quantum critical wave functions in dissipative impurity problems
• Ground state properties of sub-Ohmic spin-boson model with simultaneous diagonal and off-diagonal coupling
• Josephson-Kondo screening cloud in circuit quantum electrodynamics
• Symmetry and the critical phase of the two-bath spin-boson model: Ground-state properties
• The quantum phase transition and correlations in the multi-spin-boson model
• Quantum sweeps, synchronization, and Kibble-Zurek physics in dissipative quantum spin systems
• Sub-Ohmic spin-boson model with off-diagonal coupling: Ground state properties
• Quantum critical point of spin-boson model and infrared catastrophe in bosonic bath
• Matrix Product State Representation without explicit local Hilbert Space Truncation with Applications to the Sub-Ohmic Spin-Boson Model
• Macroscopic quantum tunneling in quartic and sextic potentials: application to a phase qubit
• The dissipative phase transition in a pair of coupled noisy two-level systems

Cited by in corpus (6)

• Quantum Phase Transitions in the Spin-Boson model: MonteCarlo Method vs Variational Approach a la Feynman
• Unveiling quantum entanglement and correlation of sub-Ohmic and Ohmic baths for quantum phase transitions in dissipative systems
• Quantum tricritical point emerging in the spin-boson model with two dissipative spins in staggered biases
• Quantum criticality of the Ohmic spin-boson model in a high dense spectrum: symmetries,quantum fluctuations and correlations
• Long-Range Order and Quantum Criticality in a Dissipative Spin Chain
• Quantum criticality in sub-Ohmic systems with three competing terms: beyond conventional spin-boson physics