Integrable quantum spin chains with free fermionic and parafermionic spectrum

Abstract

We present a general study of the large family of exact integrable quantum chains with multispin interactions introduced recently in \cite{AP2020}. The exact integrability follows from the algebraic properties of the energy density operators defining the quantum chains. The Hamiltonians are characterized by a parameter $p=1,2,\dots$ related to the number of interacting spins in the multispin interaction. In the general case the quantum spins are of infinite dimension. In special cases, characterized by the parameter $N=2,3,\dots$, the quantum chains describe the dynamics of $Z(N)$ quantum spin chains. The simplest case $p=1$ corresponds to the free fermionic quantum Ising chain ($N=2$) or the $Z(N)$ free parafermionic quantum chain. The eigenenergies of the quantum chains are given in terms of the roots of special polynomials, and for general values of $p$ the quantum chains are characterized by a free fermionic ($N=2$) or free parafermionic ($N>2$) eigenspectrum. The models have a special critical point when all coupling constants are equal. At this point the ground-state energy is exactly calculated in the bulk limit, and our analytical and numerical analyses indicate that the models belong to universality classes of critical behavior with dynamical critical exponent $z=(p+1)/N$ and specific-heat exponent $\alpha =\max \{0,1-(p+1)/N\}$.

14 pages

References in corpus (4)

• Free fermionic and parafermionic quantum spin chains with multispin interactions
• Reflection Positivity for Parafermions
• Energy spectrum and critical exponents of the free parafermion $Z_N$ spin chain
• Isospectral flows related to Frobenius-Stickelberger-Thiele polynomials

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• Free fermions beyond Jordan and Wigner
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• Integrable spin chains and cellular automata with medium range interaction
• A Brief History of Free Parafermions
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• Quantum circuits with free fermions in disguise
• Lifting integrable models and long-range interactions
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• Exact real time dynamics with free fermions in disguise
• A Graph-Theoretic Framework for Free-Parafermion Solvability
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• Critical behavior of dirty parafermionic chains
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