Quantum Phase Transition in the Spin Boson Model

Florens, Serge; Venturelli, Davide; Narayanan, R. Ganesh

doi:10.1007/978-3-642-11470-0_6

Cited by 16 publications

(12 citation statements)

References 22 publications

(34 reference statements)

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“…2(d) where we show our estimate for its 68% and 95% confidence intervals. These suggest that α c 1.25, consistent with the known analytic results [30,40,42]. We note that identifying α c precisely from the time dependence of S z is particularly challenging: since the localisation transition is in the BKT class [40], the order parameter approaches zero continuously.…”

Section: Spin-boson Phase Transitionsupporting

confidence: 82%

“…This model is known to show a rich variety of physics depending on the particular form of spectral density and system parameters chosen. When the spectral density is Ohmic, J(ω) = 2αω exp(−ω/ω c ), the model is known to exhibit a quantum phase transition in the BKT universality class [40], at a critical value of the systemenvironment coupling α = α c [30,41]. The transition takes the system from a delocalised phase below α c , where any spin excitation decays ( S z = 0 in the steady state), to a localised phase above α c ( S z = 0 in the steady state).…”

Section: Spin-boson Phase Transitionmentioning

confidence: 99%

“…Most analytic results are restricted to the regime where the cut-off frequency ω c Ω. For example, when S describes a spin-1/2 particle, the phase transition occurs at α c = 1 + O(Ω/ω c ) [30,40,42].…”

Section: Spin-boson Phase Transitionmentioning

confidence: 99%

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Efficient non-Markovian quantum dynamics using time-evolving matrix product operators

et al. 2018

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In order to model realistic quantum devices it is necessary to simulate quantum systems strongly coupled to their environment. To date, most understanding of open quantum systems is restricted either to weak system–bath couplings or to special cases where specific numerical techniques become effective. Here we present a general and yet exact numerical approach that efficiently describes the time evolution of a quantum system coupled to a non-Markovian harmonic environment. Our method relies on expressing the system state and its propagator as a matrix product state and operator, respectively, and using a singular value decomposition to compress the description of the state as time evolves. We demonstrate the power and flexibility of our approach by numerically identifying the localisation transition of the Ohmic spin-boson model, and considering a model with widely separated environmental timescales arising for a pair of spins embedded in a common environment.

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Section: Spin-boson Phase Transitionsupporting

confidence: 82%

Section: Spin-boson Phase Transitionmentioning

confidence: 99%

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Efficient non-Markovian quantum dynamics using time-evolving matrix product operators

et al. 2018

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“…In contrast, for large α, the dissipation leads to a localization of the particle in one of the two σ z eigenstates, implying a doubly degenerate ground state. On the other hand, intensive studies have recently been paid on the sub-Ohmic dissipation, which also demonstrated the QPT between localized and delocalized phases [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. In particular, the QPT could also happen in the absence of the local field (ǫ = 0) [7][8][9] from a non-degenerate ground state with zero magnetization below a critical coupling to a twofold-degenerate ground state with finite magnetization for a coupling larger than the critical value.…”

mentioning

confidence: 99%

“…Besides the incorrect employment of the state as the ground state [22], the main reason for obtaining the QPT in previous literatures [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] is the unreasonable treatment of the infrared divergence existing in the spectral functions for Ohmic and sub-Ohmic dissipations, which induced the degeneracy of the ground states in the low frequency domain. To clarify this point, we demonstrate below the potential infrared divergence in the treatments using the bath mode with continuous and discretized spectra, respectively.…”

mentioning

confidence: 99%

No Spin-Localization Phase Transition in the Spin-Boson Model without Local Field

Tao

Mang

Li³

et al. 2013

Commun. Theor. Phys.

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We explore the spin-boson model in a special case, i.e., with zero local field. In contrast to previous studies, we find no possibility for quantum phase transition (QPT) happening between the localized and delocalized phases, and the behavior of the model can be fully characterized by the even or odd parity as well as the parity breaking, instead of the QPT, owned by the ground state of the system. Our analytical treatment about the eigensolution of the ground state of the model presents for the first time a rigorous proof of no-degeneracy for the ground state of the model, which is independent of the bath type, the degrees of freedom of the bath and the calculation precision. We argue that the QPT mentioned previously appears due to incorrect employment of the ground state of the model and/or unreasonable treatment of the infrared divergence existing in the spectral functions for Ohmic and sub-Ohmic dissipations. A two-level system coupled to an environment provides a unique test-bed for fundamental interests of quantum physics. Denoting the environment by a multimode harmonic oscillator, the spin-boson model (SBM) [1, 2] presents a phenomenological description of the open quantum system, which plays an important role in quantum information science and condensed matter physics. Particularly, for the SBM at zero temperature, it has attracted intensive interests for the quantum phase transition (QPT) happening between localized and delocalized phases regarding the spin.The standard SBM Hamiltonian in units of = 1 is given by [1],where σ z and σ x are usual Pauli operators, ǫ and ∆ are, respectively, the local field (also called c-number bias [1]) and tunneling regarding the two levels of the spin. a † k and a k are creation and annihilation operators of the bath modes with frequencies ω k , and λ k is the coupling between the spin and the bath modes. The effect of the harmonic oscillator environment is reflected by the spectral function J(ω) = π k λ 2 k δ(ω − ω k ) for 0 < ω < ω c with the cutoff energy ω c . In the infrared limit, i.e., ω →0, the power laws regarding J(ω) are of particular importance. Considering the low-energy details of the spectrum, we have J(ω) = 2παω 1−s c ω s with 0 < ω < ω c and the dissipation strength α. The exponent s is responsible for different bath with super-Ohmic bath s >1, Ohmic bath s =1 and sub-Ohmic bath s <1. * Electronic address: liutao849@163.com † Electronic address: mangfeng@wipm.ac.cnThe local field ǫ introduces asymmetry in the model, which was considered to be less important than the tunneling ∆ and thereby sometimes neglected for convenience of treatments. For the Ohmic dissipation, it was mentioned [3,4] that the SBM has a delocalized and a localized zero temperature phase, separated by a Kosterlitz-Thouless (KT) transition in the case of ǫ = 0. In the delocalized phase, realized at small dissipation strength α, the non-degenerate ground state behaves like a damped tunneling particle. In contrast, for large α, the dissipation leads to a localization of the particle ...

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Quantum Phase Transition in the Spin Boson Model

Cited by 16 publications

References 22 publications

Efficient non-Markovian quantum dynamics using time-evolving matrix product operators

Efficient non-Markovian quantum dynamics using time-evolving matrix product operators

No Spin-Localization Phase Transition in the Spin-Boson Model without Local Field

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