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DOE OSTI · 1579979

Topological order in matrix Ising models

Hartnoll, Sean·Mazenc, Edward·Shi, Zhengyan
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Abstract

We study a family of models for an N_1 \times N_2 N 1 × N 2 matrix worth of Ising spins S_{aB} S a B . In the large N_i N i limit we show that the spins soften, so that the partition function is described by a bosonic matrix integral with a single ‘spherical’ constraint. In this way we generalize the results of to a wide class of Ising Hamiltonians with O(N_1,\mathbb{Z})\times O(N_2,\mathbb{Z}) O ( N 1 , ℤ ) × O ( N 2 , ℤ ) symmetry. The models can undergo topological large N N phase transitions in which the thermal expectation value of the distribution of singular values of the matrix S_{aB} S a B becomes disconnected. This topological transition competes with low temperature glassy and magnetically ordered phases.

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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICSPhysics

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Hartnoll, Sean, Mazenc, Edward, Shi, Zhengyan. 2019-12-19. Topological order in matrix Ising models. https://doi.org/10.21468/scipostphys.7.6.081

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