Classical-to-quantum crossover in the critical behavior of the transverse-field Sherrington-Kirkpatrick spin glass model

Mukherjee, Sudip; Rajak, Atanu; Chakrabarti, Bikas K.

doi:10.1103/physreve.92.042107

Cited by 20 publications

(82 citation statements)

References 22 publications

(28 reference statements)

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“…We numerically estimate the phase diagram of the quantum SK model [19]. To find the critical transverse field or temperature we use the Binder cumulant technique.…”

Section: Study Of Critical Behavior At Finite and Zero Temperaturementioning

confidence: 99%

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On the Question of Ergodicity in Quantum Spin Glass Phase and Its Role in Quantum Annealing

Mukherjee

Chakrabarti

2019

J. Phys. Soc. Jpn.

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We first review, following our earlier studies, the critical behavior of the quantum Sherrington-Kirkpatrick (SK) model at finite as well as at zero temperatures. Through the analysis of the Binder cumulant we determined the entire phase diagram of the model and from the scaling analysis of the numerical data we obtained the correlation length exponent. For both the critical Binder cumulant and the correlation length exponent, we observed a crossover from classical-to quantum-fluctuation-dominated values at a finite temperature. We studied the behavior of the order parameter distribution of the model in the glass phase (at finite and zero temperatures). Along with a classical-fluctuation-dominated nonergodic region (where the replica symmetry is broken), we also found a quantum-fluctuation-dominated low-temperature ergodic region in the spin glass phase. In this quantum-fluctuation-dominated region, the order parameter distribution has a narrow peak around its most probable value, eventually becoming a delta function in the infinite-system-size limit (indicating replica symmetry restoration or ergodicity in the system). We also found that the annealing time (to reach a very low energy level of the classical SK model) becomes practically system-size-independent when the annealing paths pass through this ergodic region. In contrast, when such paths pass through the nonergodic region, the convergence time grows rapidly with the system size. We present a new study of the autocorrelation of the spins in both ergodic and nonergodic regions. We found a significant increase in the relaxation time (and also a change in the relaxation behavior) in the classical-fluctuation-dominated (nonergodic) region compared with that in the quantum-fluctuation-dominated (ergodic) region of the spin glass phase.

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“…We numerically estimate the phase diagram of the quantum SK model [19]. To find the critical transverse field or temperature we use the Binder cumulant technique.…”

Section: Study Of Critical Behavior At Finite and Zero Temperaturementioning

confidence: 99%

“…We carry out this calculation for an interval of time T, then with the spin profile at T + 1, we repeat the same calculation for next T Monte Carlo steps. For a given system size N the autocorrelation function is [19]. The spin glass and paramagnetic phases are denoted by SG and PM, respectively.…”

Section: Study Of Spin Autocorrelation Dynamicsmentioning

confidence: 99%

On the Question of Ergodicity in Quantum Spin Glass Phase and Its Role in Quantum Annealing

Mukherjee

Chakrabarti

2019

J. Phys. Soc. Jpn.

Self Cite

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“…A recent numerical study of its critical behavior reveals the existence of two different universality classes (classical and quantum), with a crossover at a finite temperature 31 . The behavior of the energy gap for small system sizes has also been studied in detail 25,26 .…”

Section: Introductionmentioning

confidence: 99%

“…The phase diagram has also been obtained using both mean field methods 3,6,7 and QMC simulations 31,32 . A recent numerical study of its critical behavior reveals the existence of two different universality classes (classical and quantum), with a crossover at a finite temperature 31 .…”

Section: Introductionmentioning

confidence: 99%

“…Using Lanczos algorithm, some studies computed the energy gap 22,25,26 as well as physical quantities such as the Binder cumulant 31 for up to N ≈ 22, but further increase in N is hampered by the exponential increase in the dimension of the eigenvectors. The third approach is Quantum Monte Carlo (QMC) 23,24,31,32 . Unlike the previous methods, instead of including all the terms in Hilbert space, one instead performs a sampling of the states of an effective classical model in imaginary time 33 .…”

Section: Introductionmentioning

confidence: 99%

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Effects of low-lying excitations on ground-state energy and energy gap of the Sherrington-Kirkpatrick model in a transverse field

Koh

2016

Phys. Rev. B

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We present an extensive numerical study of the Sherrington-Kirkpatrick model in transverse field. Recent numerical studies of quantum spin-glasses have focused on exact diagonalization of the full Hamiltonian for small systems (≈ 20 spins). However, such exact numerical treatments are difficult to apply on larger systems. We propose making an approximation by using only a subspace of the full Hilbert space spanned by low-lying excitations consisting of one-spin flipped and two-spin flipped states. The approximation procedure is carried out within the theoretical framework of Hartree-Fock approximation and Configuration Interaction. Although not exact, our approach allows us to study larger system sizes comparable to that achievable by state of the art Quantum Monte Carlo simulations. We calculate two quantities of interest due to recent advances in quantum annealing, the ground-state energy and the energy gap between the ground and first excited state. For the energy gap, we derive a novel formula that enables it to be calculated using just the ground-state wavefunction, thereby circumventing the need to diagonalize the Hamiltonian.We calculate the scalings of the energy gap and the leading correction to the extensive part of the ground-state energy with system size, which are difficult to obtain with current methods.

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Quantum Kibble–Zurek Mechanism

Puebla

2018

Equilibrium and Nonequilibrium Aspects of Phase Transitions in Quantum Physics

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Classical-to-quantum crossover in the critical behavior of the transverse-field Sherrington-Kirkpatrick spin glass model

Cited by 20 publications

References 22 publications

On the Question of Ergodicity in Quantum Spin Glass Phase and Its Role in Quantum Annealing

On the Question of Ergodicity in Quantum Spin Glass Phase and Its Role in Quantum Annealing

Effects of low-lying excitations on ground-state energy and energy gap of the Sherrington-Kirkpatrick model in a transverse field

Quantum Kibble–Zurek Mechanism

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