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Physics Letters A

Comment on “Quantum mechanical description of thermal equilibrium states as eigenstates of relative-phase interactions” by Kobayashi

M. Dugić

Published Oct 1, 1997• 0 citations
Publisher
DOI
10.1016/s0375-9601(97)00601-4

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Eigenstates of the annihilation type operator U = C + iS, where C and S are the ``cosine'' and ``sine'' operators for harmonic oscillator phase, are shown to be closely related to thermal equilibrium states of the oscillator and to provide a new interpretation of the thermal equilibrium density operator. The problem of creating such states is considered and a general theorem is established leading to the construction of interaction Hamiltonians which transform the eigenstates of U among themselves and, in particular, create them from the oscillator ground state. These Hamiltonians lead to representations of the Lie algebras of O(2,1) and O(3). It is suggested that the mathematical technique used, in which generalized U-type operators provide the link between a group and its representations, has its own intrinsic interest for the study of Lie groups.
Understanding how microscopic few-body interactions give rise to thermal behavior in isolated quantum many-body systems remains a central challenge in nonequilibrium statistical mechanics. While individual energy eigenstates are expected to reproduce thermal equilibrium values, analytic access to highly entangled thermal eigenstates of nonintegrable Hamiltonians remains scarce. In this Letter, we construct exact infinite-temperature eigenstates of generically nonintegrable two-body Hamiltonians using stabilizer states. These states can fully reproduce thermal expectation values for all spatially local observables, extending previously known Bell-pair-based constructions to a broader class. At the same time, we prove a sharp no-go theorem: stabilizer eigenstates of two-body Hamiltonians cannot satisfy microscopic thermal equilibrium for all four-body observables. This bound is tight, as we explicitly construct a translationally invariant Hamiltonian whose stabilizer eigenstate is thermal for all two-body and three-body observables as well as all spatially local observables. Our results suggest that reproducing higher-order thermal correlations requires nonstabilizer degrees of freedom, providing analytic insight into the interplay between interaction locality, microscopic thermal equilibrium, and quantum computational complexity.