Renormalization of the anisotropic linearXYmodel

Abstract

The renormalization scheme recently proposed by White is applied to the d = 1 anisotropic XY model in a transverse field (AXY). It is found that this scheme offers a distinct improvement over standard techniques as far as the computation of the ground state is concerned. However, compared to the Ising model in a transverse Geld, on account of more complicated symmetries the AXY demands more precautions during the construction of a renormalization-group transformation. The new method predicts deGnitely better the location of the phase transition in the XY-like region than in the Ising-like region, but only in the Ising-like region is there any progress for the critical exponent a.

Phase diagram of the antiferromagneticXXZmodel in the presence of an external magnetic field

“…The phase diagram of the obtained RG-flow(eqs. (10,11)) is depicted in fig.2. This phase diagram consists of three different phases, partially magnetized (PM), classical anti-ferromagnetic(AFI) and saturated ferromagnetic (SFM) phases.…”

“…At ∆ = 0, even in the presence of magnetic field, the model can be mapped by Jordan-Wigner transformation to free-fermions [17], which is exactly solvable. This system has also been studied within the RG formalism [11].…”

“…The Ising model in a transverse field (ITF) and anisotropic XY model in a transverse field (AXYTF) have been studied in [10,11] using both standard RG and DMRG methods.…”

Entanglement renormalization of anisotropic XY model

“…It is known that the accuracy of the traditional RSRG can be improved by increasing the block size. 15,16,18,21,22 This fact is justified by the results without disentangler. As shown in the table, x c (1) is improved from 1.291 of the 3-site block scheme to 1.233 of the 5-site block scheme.…”

“…[12][13][14] It also provides a test field for new numerical schemes. 15,16 The phase diagrams and the critical exponents of AXY and ITF have been obtained using various RSRG and DMRG schemes. In this paper, we study these models by using different MERA schemes.…”