Two-dimensional random-bond Ising model, free fermions, and the network model

  title={Two-dimensional random-bond Ising model, free fermions, and the network model},
  author={Florian Merz and J. T. Chalker},
  journal={Physical Review B},
We develop a recently proposed mapping of the two-dimensional Ising model with random exchange (RBIM) via the transfer matrix, to a network model for a disordered system of noninteracting fermions. The RBIM transforms in this way to a localization problem belonging to one of a set of nonstandard symmetry classes, known as class D; the transition between paramagnet and ferromagnet is equivalent to a delocalization transition between an insulator and a quantum Hall conductor. We establish the… 

Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code

Two implementations of the optimal error correction algorithm known as the maximum likelihood decoder (MLD) for the 2D surface code with a noiseless syndrome extraction are described and a significant reduction of the logical error probability for $\chi\ge 4$.

Quantum information and statistical mechanics: an introduction to frontier

This is a short review on an interdisciplinary field of quantum information science and statistical mechanics. We first give a pedagogical introduction to the stabilizer formalism, which is an

Strong-Disorder Paramagnetic-Ferromagnetic Fixed Point in the Square-Lattice ±J Ising Model

We consider the random-bond ±J Ising model on a square lattice as a function of the temperature T and of the disorder parameter p (p=1 corresponds to the pure Ising model). We investigate the

Nishimori's cat: stable long-range entanglement from finite-depth unitaries and weak measurements

In the field of monitored quantum circuits, it has remained an open question whether finite-time protocols for preparing long-range entangled (LRE) states lead to phases of matter which are stable to

Morphing Quantum Codes

A morphing procedure is introduced that can be used to generate new quantum codes from existing quantum codes, including the 15-qubit Reed-Muller code, and a family of hybrid color-toric codes is constructed by morphing the color code.

Analyticity of the energy in an Ising spin glass with correlated disorder

  • H. Nishimori
  • Physics
    Journal of Physics A: Mathematical and Theoretical
  • 2021
The average energy of the Ising spin glass is known to have no singularity along a special line in the phase diagram although there exists a critical point on the line. This result on the model with

Multicriticality of two-dimensional class-D disordered topological superconductors

A generic two-dimensional disordered topological superconductor in symmetry class D exhibits rich phenomenology and multiple phases: diffusive thermal metal (DTM), Anderson insulator (AI), and

Enhanced noise resilience of the surface–Gottesman-Kitaev-Preskill code via designed bias

It is shown that Gaussian encodings of individual modes can enhance concatenated codes and improve the noise tolerance of this surface-GKP code with respect to (Gaussian) displacement errors.

Quantum Hall Network Models as Floquet Topological Insulators.

This work shows that, despite their topologically distinct origins, IQH and chiral Floquet topology-changing transitions share identical universal scaling properties.

Simulating Floquet topological phases in static systems

We show that scattering from the boundary of static, higher-order topological insulators (HOTIs) can be used to simulate the behavior of (time-periodic) Floquet topological insulators. We consider



Exactly solved models in statistical mechanics

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