Solvable model of the quantum spin glass in a transverse field

Goldschmidt, Yadin Y.

doi:10.1103/physrevb.41.4858

Cited by 114 publications

(172 citation statements)

References 22 publications

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“…However, short-range models have O(1) local fields, and in fact, so do power-law and infinite-range systems with general p-body interactions. This suggests that the eigenstate-localized phase of the QREM is an exceptional case among long-range models: strict configuration-space localization cannot exist in any model with O(1) local fields, since the introduction of quantum dynamics causes resonant fluctuations.In this paper, we study the eigenstate properties of the quantum p-spin models [25][26][27][28]. Over the past four decades, these models have become paradigms for the mean-field theory of spin glasses [29][30][31][32] Sherrington-Kirkpatrick model (p = 2) [33,34].…”

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confidence: 99%

“…s c ( ) is the entropy density within c (which is strictly less than s eq ( )), and g c is a smooth, cluster-dependent O(1) function. More physically, such non-ergodic eigenstates are thermal within a cluster but not thermal in configuration space as a whole.Concretely, the quantum p-spin models are defined by [25] that the thermodynamic free energy of H p approaches that of the QREM as p increases. The eigenstate phases of H p do as well, yet the eigenstates are never localized at any finite p. They are instead non-ergodic, in a manner that comes to resemble localization as p increases.…”

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confidence: 99%

“…In this paper, we study the eigenstate properties of the quantum p-spin models [25][26][27][28]. Over the past four decades, these models have become paradigms for the mean-field theory of spin glasses [29][30][31][32] Sherrington-Kirkpatrick model (p = 2) [33,34].…”

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confidence: 99%

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Clustering of Nonergodic Eigenstates in Quantum Spin Glasses

et al. 2017

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The two primary categories for eigenstate phases of matter at finite temperature are manybody localization (MBL) and the eigenstate thermalization hypothesis (ETH). We show that in the paradigmatic quantum p-spin models of spin-glass theory, eigenstates violate ETH yet are not MBL either. A mobility edge, which we locate using the forward-scattering approximation and replica techniques, separates the non-ergodic phase at small transverse field from an ergodic phase at large transverse field. The non-ergodic phase is also bounded from above in temperature, by a transition in configuration-space statistics reminiscent of the clustering transition in spin-glass theory. We show that the non-ergodic eigenstates are organized in clusters which exhibit distinct magnetization patterns, as characterized by an eigenstate variant of the Edwards-Anderson order parameter.Many systems under experimental investigation as platforms for many-body localization (MBL) [1][2][3][4][5][6][7][8][9] have long-range interactions that mediate the direct transport of excitations. This includes disordered electronic materials [10,11], ion traps [12], interacting NV centers in diamond [13,14], and superconducting qubit devices developed for adiabatic quantum computing [15][16][17]. In sufficiently long-ranged systems, the proliferation of longdistance resonances precludes quantum mechanical localization [18][19][20][21][22], an intuitive result strongly supported by analytic work over the last half century. Nevertheless, the quantum Random Energy Model (QREM), an infiniterange spin glass, was recently shown to exhibit a phase with localized eigenstates at finite energy density [23,24]. The QREM provides an analytically tractable framework for studying mobility edges and configuration-space localization. This raises the obvious question of how localization survives despite the infinite-range interactions and what role it plays in more realistic long-range systems.Some insight comes from considering the distribution of local fields -i.e., the energy required to flip one of the system's N spins relative to a given configuration. In the QREM, flipping a spin typically changes the energy by O(N ). Thus the quantum fluctuations which lead to the proliferation of resonances are strongly suppressed. However, short-range models have O(1) local fields, and in fact, so do power-law and infinite-range systems with general p-body interactions. This suggests that the eigenstate-localized phase of the QREM is an exceptional case among long-range models: strict configuration-space localization cannot exist in any model with O(1) local fields, since the introduction of quantum dynamics causes resonant fluctuations.In this paper, we study the eigenstate properties of the quantum p-spin models [25][26][27][28]. Over the past four decades, these models have become paradigms for the mean-field theory of spin glasses [29][30][31][32] Sherrington-Kirkpatrick model (p = 2) [33,34]. The QREM corresponds to the p → ∞ limit in many senses, but the local-field distrib...

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Clustering of Nonergodic Eigenstates in Quantum Spin Glasses

et al. 2017

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“…Although this change survives even if we take the higher-order correlations into account as we show in the following, it is not clear whether it corresponds to the phase-transition point or not. For example, in the random energy model 16 the corresponding phase transition is of first order and it is not possible to determine the transition point from perturbative calculation (see Sec. III C for detailed calculations).…”

Section: B Self-consistent Equation In Linear Ordermentioning

confidence: 99%

“…At p → ∞ this model is known as the random energy model and exhibits first-order phase transition between the CP and the QP phases. 16 The imaginary-time-correlation function at the QP phase can be calculated from the self-consistent equation in terms of χ(τ ),…”

Section: Classical and Quantum Paramagnetic Phasementioning

confidence: 99%

Dynamical correlations in the Sherrington-Kirkpatrick model in a transverse field

Takahashi

Takeda

2008

Phys. Rev. B

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We calculate the real-time-correlation function of the Sherrington-Kirkpatrick spin-glass model in a transverse field. Using a careful analysis of the perturbative expansion of the functionalintegral representation, we derive the asymptotic form of the correlation function. In contrast to the previous works, we find for large transverse field a power-law decay of the correlation with time t as t −3/2 at zero temperature and t −2 at infinite temperature. At the small field region, we also find a significant change in the correlation which comes from the structural difference between two paramagnetic phases.

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