Weak universality, quantum many-body scars, and anomalous infinite-temperature autocorrelations in a one-dimensional spin model with duality

Udupa, Adithi; Sur, Samudra; Nandy, Sourav; Sen, Arnab; Sen, Diptiman

doi:10.1103/PhysRevB.108.214430

Weak universality, quantum many-body scars, and anomalous infinite-temperature autocorrelations in a one-dimensional spin model with duality

Jul 20, 2023

23 pages

Published in:

Phys.Rev.B 108 (2023) 21, 214430

Published: Dec 1, 2023

e-Print:

2307.11161 [cond-mat.stat-mech]

DOI:

10.1103/PhysRevB.108.214430 (publication)

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Abstract: (APS)

We study a one-dimensional spin-

1 / 2

model with three-spin interactions and a transverse magnetic field

h

. The model is known to have a

Z_{2} \times Z_{2}

symmetry and a duality between

h

and

1 / h

. The self-dual point at

h = 1

is a quantum critical point with a continuous phase transition. We compute the critical exponents

z, β, γ

, and

ν

, and the central charge

c

numerically using exact diagonalization (ED) for systems with periodic boundary conditions. We find that both

z

and

c

are equal to 1, implying that the critical point is governed by a conformal field theory with a marginal operator. The values obtained for

β / ν, γ / ν

, and

ν

from ED suggest that the model exhibits Ashkin-Teller criticality with an effective coupling that is intermediate between the four-state Potts model and two decoupled transverse field Ising models. A more careful analysis on much larger systems but with open boundaries using density-matrix renormalization group (DMRG) calculations, however, reveals important additive and multiplicative logarithmic corrections at and near criticality, and we present evidence that the self-dual point may be in the same universality class as the four-state Potts model. An energy level spacing analysis shows that the model is not integrable. For a system with an even number of sites and periodic boundary conditions, there are exact mid-spectrum zero-energy eigenstates whose number grows exponentially with the system size. A subset of these eigenstates have wave functions that are independent of the value of

h

and have unusual entanglement structures; hence these can be considered to be quantum many-body scars. The number of such quantum scars scales at least linearly with system size. Finally, we study the infinite-temperature autocorrelation functions at sites close to one end of an open system. We find that some of the autocorrelators relax anomalously in time, with pronounced oscillations and very small decay rates if

h ≫ 1

or

h ≪ 1

. If

h

is close to the critical point, the autocorrelators decay quickly to zero except for an autocorrelator at the end site.

Note:

23 pages, 20 figures; corrected some typos

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