Anomalous bulk behaviour in the free parafermion $Z(N)$ spin chain

Abstract

We demonstrate using direct numerical diagonalization and extrapolation methods that boundary conditions have a profound effect on the bulk properties of a simple $Z(N)$ model for $N\ge 3$ for which the model hamiltonian is non-hermitian. For $N=2$ the model reduces to the well known quantum Ising model in a transverse field. For open boundary conditions the $Z(N)$ model is known to be solved exactly in terms of free parafermions. Once the ends of the open chain are connected by considering the model on a ring, the bulk properties, including the ground-state energy per site, are seen to differ dramatically with increasing $N$. Other properties, such as the leading finite-size corrections to the ground-state energy, the mass gap exponent and the specific heat exponent, are also seen to be dependent on the boundary conditions. We speculate that this anomalous bulk behaviour is a topological effect.

8 pages, 8 figures, minor changes

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Cited by in corpus (8)

• Free fermionic and parafermionic quantum spin chains with multispin interactions
• Integrable quantum spin chains with free fermionic and parafermionic spectrum
• Free-parafermionic $Z(N)$ and free-fermionic $XY$ quantum chains
• Exceptional Points in the Baxter-Fendley Free Parafermion Model
• A Brief History of Free Parafermions
• Some ground-state expectation values for the free parafermion Z(N) spin chain
• A Graph-Theoretic Framework for Free-Parafermion Solvability
• Critical behavior of dirty parafermionic chains