Split Property and Fermionic String Order
We show split property of gapped ground states for Fermion systems on a one-dimensional lattice and clarify mathematical meaning of string order of fermions.
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arXiv subjects
Taku Matsui
Publications and source records attributed to Taku Matsui.
KMS States of Weakly Coupled Anharmonic Crystals and the Resolvent CCR Algebra
We consider equilibrium states of weakly coupled anharmonic quantum oscillators on Z. We consider the Resolvent CCR Algebra introduced by D.Buchholtz and H.Grundling, and we show that the infinite volume limit of equilibrium states satisfies the KMS (Kubo-Martin-Schwinger) condition with good regularity(= locally Fock representation). Uniqueness of the KMS states is proven as well.
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Kakutani Dichotomy on Free States
Two quasi-free states on a CAR or CCR algebra are shown to generate quasi-equivalent representations unless they are disjoint.
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Boundedness of Entanglement Entropy,and Split Property of Quantum Spin Chains
We show the boundedness of entanglement entropy for (bipartite) pure states of quantum spin chains implies split property of subsystems. As a corollary the infinite volume ground states for 1-dim spin chains with the spectral gap between the ground state energy and the rest of spectrum have the split property. We see gapless excitation exists for the spinless Fermion on $\bfZ$ if the ground state is non-trivial and translationally invariant and the U(1) gauge symmetry is unbroken. Here we do not assume uniqueness of ground states for all finite volume Hamiltonians.
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On Spectral Gap,U(1) Symmetry and Split Property in Quantum Spin Chains
We consider a class of ground states for quantum spin chains on an integer lattice. First we show that presence of the spectral gap between the ground state energy and the rest of spectrum implies the split property of certain subsystems.As a corollary, we show that gapless excitation exists for spinless Fermion if the pure gauge invariant ground state is non-trivial and translationally invariant.
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On Haag Duality for Pure States of Quantum Spin Chain
We consider quantum spin chains and their translationally invariant pure states. We prove Haag duality for quasilocal observables localized in semi-infinite intervals when the von Neumann algebras generated by observables localized in these intervals are not type I.
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Note on MacLennan-Zubarev Ensembles and QuasiStatic Processes
Relation between natural nonequilibrium steady states of Ruelle and MacLennan-Zubarev ensembles is discussed for a system consisting of $M$ infinitely extended systems coupled with a small system. And a characterization of quasistatic processes is investigated for a small system coupled with a single reservoir.
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BEC of Free Bosons on Networks
We consider free Bosons hopping on a network(infinite graph). The condition for Bose-Einstein condensation is given in terms of the random walk on a graph. In case of periodic lattices, we also consider Boson moving in an external periodic potential and obatined the criterion for Bose-Einstein condensation.
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On Quasifree Representations of Infinite Dimensional Symplectic Group
We consider an infinite dimensional generalization of Metaplectic representations (Weil representations) for the (double covering of) symplectic group. Given quasifree states of an infinite dimensional CCR algebra, projective unitary representations of the infinite dimensional symplectic group are constructed via unitary implementors of Bogoliubov automorphisms. Complete classification of these representations up to quasi-equivalence is obtained.
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On the Algebra of Fluctuation in Quantum Spin Chains
We present a proof of the central limit theorem for a pair of mutually non-commuting operators in mixing quantum spin chains. The operators are not necessarily strictly local but quasi-local. As a corollary we obtain a direct construction of the time evolution of the algebra of normal fluctuation for Gibbs states of finite range interactions on a one-dimensional lattice. We show that the state of the algebra of normal fluctuation satisfies the $β$-KMS condition if the microscopic state is a $β$-KMS state.
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