Heisenberg Model, Bethe Ansatz, and Random Walks
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منابع مشابه
A direct calculation of the free energy from the Bethe ansatz equation for the Heisenberg model
A direct calculation of the free energy from the Bethe ansatz equation for the Heisenberg model. Abstract Thermodynamics of the XXX Heisenberg model is studied. The trace of the Boltz-mann weight with respect to the Hilbert space is taken in the thermodynamic limit with the number of up-spins being fixed. The expression of the trace gives an explanation why the correct thermodynamic quantities ...
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We examine the question of whether Bethe’s ansatz reproduces all states in the periodic Heisenberg XXZ and XXX spin chains. As was known to Bethe himself, there are states for which the Bethe momenta kn diverge: these are in fact the simplest examples of “string” solutions. The coefficients of the Bethe wavefunction, too, diverge. When there are only two down spins in the system (the case consi...
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The slq(2)-quantum group invariant spin 1/2 XXZ-Heisenberg model with open boundary conditions is investigated by means of the Bethe ansatz. As is well known, quantum groups for q equal to a root of unity possess a finite number of “good” representations with non-zero q-dimension and “bad” ones with vanishing q-dimension. Correspondingly, the state space of an invariant Heisenberg chain decompo...
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The XXX Heisenberg model is studied at finite temperature. The free energy is derived without recourse to Thermal Bethe Ansatz method and Quantum Transfer Matrix method. The result perfectly agrees with the free energy derived by Thermal Bethe Ansatz method. An explicit expression of the cluster expansion coefficient in arbitrary order is presented for the first time.
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