Existence of Replica-Symmetry Breaking in Quantum Glasses.

@article{Leschke2021ExistenceOR,
  title={Existence of Replica-Symmetry Breaking in Quantum Glasses.},
  author={Hajo Leschke and Chokri Manai and Rainer Ruder and Simone Warzel},
  journal={Physical review letters},
  year={2021},
  volume={127 20},
  pages={
          207204
        }
}
By controlling quantum fluctuations via the Falk-Bruch inequality we give the first rigorous argument for the existence of a spin-glass phase in the quantum Sherrington-Kirkpatrick model with a "transverse" magnetic field if the temperature and the field are sufficiently low. The argument also applies to the generalization of the model with multispin interactions, sometimes dubbed as the transverse p-spin model. 
View With Semantic Reader
5 Citations
Background Citations
3

Figures from this paper

5 Citations

Citation Type

Citation Type

The de Almeida–Thouless Line in Hierarchical Quantum Spin Glasses
We determine explicitly and discuss in detail the effects of the joint presence of a longitudinal and a transversal (random) magnetic field on the phases of the Random Energy Model and its…
Universality of replica-symmetry breaking in the transverse field Sherrington-Kirkpatrick model
The existence theorem for replica-symmetry breaking (RSB) in the transverse field SherringtonKirkpatrick (SK) model is extended to the model with a general random exchange interactions. The relation…
A Variational Ansatz for the Ground State of the Quantum Sherrington-Kirkpatrick Model
We present an ansatz for the ground states of the Quantum Sherrington-Kirkpatrick model, a paradigmatic model for quantum spin glasses. Our ansatz, based on the concept of generalized coherent…
Spectral Analysis of the Quantum Random Energy Model
The Quantum Random Energy Model (QREM) is a random matrix of Anderson-type which describes effects of a transversal magnetic field on Derrida’s spin glass. The model exhibits a glass phase as well as…
Development of research network on Quantum Annealing Computation and Information using Google Scholar data
We build and analyze the network of hundred top cited nodes (research papers and books from Google Scholar; strength or citation of the nodes range from about 44000 upto 100) starting early 1980 to…

References

SHOWING 1-10 OF 61 REFERENCES
Quantum fluctuations in an ising spin glass with transverse field
Phase Transitions in Quantum Spin Systems with Isotropic and Nonisotropic Interactions
We prove the existence of spontaneous magnetization at sufficiently low temperature, and hence of a phase transition, in a variety of quantum spin systems in three or more dimensions. The isotropic…
Thermodynamics and Universality for Mean Field Quantum Spin Glasses
We study aspects of the thermodynamics of quantum versions of spin glasses. By means of the Lie-Trotter formula for exponential sums of operators, we adapt methods used to analyze classical spin…
Replica-symmetry breaking for the Ising spin glass in a transverse field.
TLDR
Internal energy, entropy, and magnetic susceptibility are calculated in order to investigate the quality of both the replica-symmetric and the replica -symmetry-broken theories.
Some observations on the mean-field theory of spin glasses
A finite negative ground state energy and a non-negative ground state entropy appear to be incompatible unless linear response theory is abandoned in the spin glass phase. Various approaches using…
Ising spin glass in a transverse field: Replica-symmetry-breaking solution.
TLDR
It is demonstrated that replica symmetry (RS) has to be broken in the spin-glass phase by comparing the free energies of the RSB and RS solutions.
Stability of the quantum Sherrington-Kirkpatrick spin glass model.
TLDR
It is found that the replica symmetric solution is unstable down to zero temperature, in contrast to some previous claims, and so there is not only a line of transitions in the (longitudinal) field-temperature plane but also a quantum de Almeida-Thouless (QuAT) line in the transverse field-longitudinal field plane at T=0.
Phase Diagram of the Quantum Random Energy Model
We prove Goldschmidt’s formula (Goldschmidt in Phys Rev B 47:4858–4861, 1990) for the free energy of the quantum random energy model. In particular, we verify the location of the first order and the…
Spin glasses with p-spin interactions
The order parameter for spin glasses: a function on the interval 0-1
The breaking of the replica symmetry in spin glasses is studied. It is found that the order parameter is a function on the interval 0-1. This approach is used to study the Sherrington-Kirkpatrick…
...
...