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This study provides a complete finite-size spectral solution for the periodic non-Hermitian Baxter-Fendley chain, resolving a longstanding theoretical gap regarding looped systems versus open boundaries. By utilizing operator-valued matching polynomials, the researchers identified two distinct critical coupling points for homogeneous chains with N=3, revealing greater complexity at phase transitions than previously understood. This advancement offers an efficient method for calculating ground state energies without exhaustive computation, contributing directly to the fundamental understanding of non-Hermitian quantum many-body systems.

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Researchers Map Baxter-Fendley Chain’s Entire Energy Spectrum

Quantum ZeitgeistSeptember 15, 20264 min read

For homogeneous chains with N=3, predictions now reveal two distinct points where phase transitions occur, diverging from previous findings which identified only one such instance on open boundaries. This complete spectral solution for the periodic Baxter-Fendley chain, previously known solely for its open counterpart, is achieved through an operator-valued matching polynomial generating conserved quantities. The method also offers efficient calculation of ground state energies without exhaustive computation.

Yuguan Li of National University and colleagues have obtained a complete finite-size spectral solution for the periodic non-Hermitian Baxter-Fendley ZN clock chain, differing from previous incomplete solutions. Employing operator-valued matching polynomials, the team demonstrated that conserved quantities are generated and a cyclic Yang-Baxter transfer matrix is realised, enabling full calculation of energy levels. Specifically, for homogeneous chains where N equals three, their work predicts two reciprocal critical couplings compared to one previously known for…

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