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In this paper we give an exact infinite-series expression for the bi-partite entanglement entropy of the quantum Ising model
in the ordered regime, both with a boundary magnetic field and in infinite volume. This generalizes and extends previous results
involving the present authors for the bi-partite entanglement entropy of integrable quantum field theories, which exploited
the generalization of the form factor program to branch-point twist fields. In the boundary case, we isolate in a universal
way the part of the entanglement entropy which is related to the boundary entropy introduced by Affleck and Ludwig, and explain
how this relation should hold in more general QFT models. We provide several consistency checks for the validity of our form
factor results, notably, the identification of the leading ultraviolet behaviour both of the entanglement entropy and of the
two-point function of twist fields in the bulk theory, to a great degree of precision by including up to 500 form factor contributions. 相似文献
2.
L. S. Lussier C. Sandorfy H. OA L E-Thanh D. Vocelle 《Photochemistry and photobiology》1987,45(S1):801-808
Abstract— The Fourier-transform infrared spectra of chloroform-d solutions of conjugated imines CH3 CH=CHCH=NCH(CH3 )2 and CH3 CH2 CH=CHCH=CHCH=NCH(CH3 )2 and the related protonated species with HCl, HBr, HI, trichloro, dichloro, monobromo and monochloroacetic acids or propionic acid are presented. The effects of conjugation and protonation are examined. The results show that conjugation slightly increases the basicity of the Schiff bases. HCl, HBr and HI protonate the Schiff bases completely. The carboxylic acids protonate partially depending on their p K a , values. When the Schiff base contains two (or more) C=C bonds conjugated with C=N, the main C=C stretching band undergoes a strong intensification showing that sizeable dipole moment variations occur along the conjugated chain. 相似文献
3.
In this paper we compute the leading correction to the bipartite entanglement entropy at large sub-system size, in integrable
quantum field theories with diagonal scattering matrices. We find a remarkably universal result, depending only on the particle
spectrum of the theory and not on the details of the scattering matrix. We employ the “replica trick” whereby the entropy
is obtained as the derivative with respect to n of the trace of the nth power of the reduced density matrix of the sub-system, evaluated at n=1. The main novelty of our work is the introduction of a particular type of twist fields in quantum field theory that are
naturally related to branch points in an n-sheeted Riemann surface. Their two-point function directly gives the scaling limit of the trace of the nth power of the reduced density matrix. Taking advantage of integrability, we use the expansion of this two-point function
in terms of form factors of the twist fields, in order to evaluate it at large distances in the two-particle approximation.
Although this is a well-known technique, the new geometry of the problem implies a modification of the form factor equations
satisfied by standard local fields of integrable quantum field theory. We derive the new form factor equations and provide
solutions, which we specialize both to the Ising and sinh-Gordon models. 相似文献
4.
We consider the bipartite entanglement entropy of ground states of extended quantum systems with a large degeneracy. Often, as when there is a spontaneously broken global Lie group symmetry, basis elements of the lowest-energy space form a natural geometrical structure. For instance, the spins of a spin-1/2 representation, pointing in various directions, form a sphere. We show that for subsystems with a large number m of local degrees of freedom, the entanglement entropy diverges as d/2 logm, where d is the fractal dimension of the subset of basis elements with nonzero coefficients. We interpret this result by seeing d as the (not necessarily integer) number of zero-energy Goldstone bosons describing the ground state. We suggest that this result holds quite generally for largely degenerate ground states, with potential applications to spin glasses and quenched disorder. 相似文献
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