Tunable quantum spin chain with three-body interactions

Adhikari, Khagendra; Beach, K. S. D.

doi:10.1103/physrevb.102.184415

Cited by 3 publications

(1 citation statement)

References 54 publications

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“…The Fredkin model, on the other hand, makes use of three-body terms that break the spin-rotationsymmetry by picking out a special direction in spin space. We have proposed a tunable model [20,27] (in the parameter λ) that interpolates between the Fredkin spin chain (at λ = 0) and the conventional ferromagnetic (λ = −1) and antiferromagnetic (λ = 1) quantum Heisenberg models. Recent work has appeared [11] that addresses the ferromagnetic side (λ < 0) of this model.…”

Section: A Modelmentioning

confidence: 99%

Deforming the Fredkin spin chain away from its frustration-free point

Adhikari

Beach

2019

Phys. Rev. B

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The Fredkin model describes a spin-half chain segment subject to three-body, correlated-exchange interactions and twisted boundary conditions. The model is frustration-free, and its ground state wave function is known exactly. Its low-energy physics is that of a strong xy ferromagnet with gapless excitations and an unusually large dynamical exponent. We study a generalized spin chain model that includes the Fredkin model as a special tuning point and otherwise interpolates between the conventional ferromagnetic and antiferromagnetic quantum Heisenberg models. We solve for the low-lying states, using exact diagonalization and density-matrix renormalization group calculations, in order to track the properties of the system as it is tuned away from the Fredkin point; we also present exact analytical results that hold right at the Fredkin point. We identify a zero-temperature phase diagram with multiple transitions and unexpected ordered phases. The Fredkin ground state turns out to be particularly brittle, unstable to even infinitesimal antiferromagnetic frustration. We remark on the existence of an "anti-Fredkin" point at which all the contributing spin configurations have a spin structure exactly opposite to those in the Fredkin ground state. arXiv:1805.00532v3 [cond-mat.str-el]

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Section: A Modelmentioning

confidence: 99%

Deforming the Fredkin spin chain away from its frustration-free point

Adhikari

Beach

2019

Phys. Rev. B

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Slow dynamics of the Fredkin spin chain

Adhikari

Beach

2021

Phys. Rev. B

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The dynamical behavior of a quantum many-particle system is characterized by the lifetime of its excitations. When the system is perturbed, observables of any non-conserved quantity decay exponentially, but those of a conserved quantity relax to equilibrium with a power law. Such processes are associated with a dynamical exponent 𝑧 that relates the spread of correlations in space and time. We present numerical results for the Fredkin model, a quantum spin chain with a three-body interaction term, which exhibits an unusually large dynamical exponent. We discuss our efforts to produce a reliable estimate 𝑧 3.18(2) through direct simulation of the quantum evolution and to explain the slow dynamics in terms of an excited bond that executes a constrained random walk in Monte Carlo time.

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Anomalous hydrodynamics in a class of scarred frustration-free Hamiltonians

Richter

Pal

2022

Phys. Rev. Research

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Tunable quantum spin chain with three-body interactions

Cited by 3 publications

References 54 publications

Deforming the Fredkin spin chain away from its frustration-free point

Deforming the Fredkin spin chain away from its frustration-free point

Slow dynamics of the Fredkin spin chain

Anomalous hydrodynamics in a class of scarred frustration-free Hamiltonians

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