Thermodynamics of a dilute XX chain in a field
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RDER, DISORDER, AND PHASE TRANSITION IN CONDENSED SYSTEM
Thermodynamics of a Dilute XX Chain in a Field1 P. N. Timonin* Physics Research Institute, Southern Federal University, Rostov-on-Don, 344090 Russia *e-mail: [email protected] Received October 21, 2015
Abstract—Gapless phases in ground states of low-dimensional quantum spin systems are rather ubiquitous. Their peculiarity is a remarkable sensitivity to external perturbations due to permanent criticality of such phases manifested by a slow (power-low) decay of pair correlations and the divergence of the corresponding susceptibility. A strong influence of various defects on the properties of the system in such a phase can then be expected. Here, we consider the influence of vacancies on the thermodynamics of the simplest quantum model with a gapless phase, the isotropic spin-1/2 XX chain. The existence of the exact solution of this model gives a unique opportunity to describe in detail the dramatic effect of dilution on the gapless phase—the appearance of an infinite series of quantum phase transitions resulting from level crossing under the variation of a longitudinal magnetic field. We calculate the jumps in the field dependences of the ground-state longitudinal magnetization, susceptibility, entropy, and specific heat appearing at these transitions and show that they result in a highly nonlinear temperature dependence of these parameters at low T. Also, the effect of enhancement of the magnetization and longitudinal correlations in the dilute chain is established. The changes of the pair spin correlators under dilution are also analyzed. The universality of the mechanism of the quantum transition generation suggests that similar effects of dilution can also be expected in gapless phases of other low-dimensional quantum spin systems. DOI: 10.1134/S1063776116060224
1. INTRODUCTION The discovery of the equivalence of XY spin chains with spin 1/2 to free fermions [1] was a breakthrough in the studies of quantum phase transitions. Such a transition takes place in the XY chain at T = 0 under a variation of the transverse field H when its modulus becomes equal to the modulus of the average nearestneighbor exchange J = (Jx + Jy)/2, JxJy > 0 [1–5]. Usually, it features the ordinary scaling behavior with the order parameter being the magnetization component with the largest exchange, i.e., Mx if |Jx| > |Jy|. Then Mx vanishes at |H| > |J| and only Mz along the field exists. Apparently, this scenario does not hold in the special case of an isotropic (XX) chain with Jx = Jy = J, where rotational symmetry and low dimension makes Mx = My = 0 at all H [1–5]. Nevertheless, the XX chain also experiences a ground-state quantum transition at |H| = |J| from a saturated phase with Mz = 1/2sign(H) into the so-called quasi-long-range-ordered (QLRO) phase at |H| < |J| characterized by the vanishing of the gap between the ground and excited states in the energy spectrum of free fermions [5–7] and a powerlaw decay of spin correlators [8–10]. Thus, the XX chain is always in a critical sta
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