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arXiv:1704.03420 · Physical review. B./Physical review. B

Long-range interactions in antiferromagnetic quantum spin chains

Barbara Bravo, D. C. Cabra, F. A. Gómez Albarracín, G. L. Rossini

Published Aug 25, 2017• 5 citations
arXivHTMLPDF

Abstract

We study the role of long-range dipolar interactions on antiferromagnetic spin chains, from the classical $S\ensuremath{\rightarrow}\ensuremath{\infty}$ limit to the deep quantum case $S=1/2$, including a transverse magnetic field. To this end, we combine different techniques such as classical energy minima, classical Monte Carlo, linear spin waves, bosonization, and density matrix renormalization group (DMRG). We find a phase transition from the already reported dipolar ferromagnetic region to an antiferromagnetic region for high enough antiferromagnetic exchange. Thermal and quantum fluctuations destabilize the classical order before reaching magnetic saturation in both phases, and also close to zero field in the antiferromagnetic phase. In the extreme quantum limit $S=1/2$, extensive DMRG computations show that the main phases remain present with transition lines to saturation significatively shifted to lower fields, in agreement with the bosonization analysis. The overall picture maintains a close analogy with the phase diagram of the anisotropic XXZ spin chain in a transverse field.

DOI
10.1103/physrevb.96.054441

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We study the role of long-range dipolar interactions on antiferromagnetic spin chains, from the classical S\ensuremath→\ensuremath∞S\ensuremath{\rightarrow}\ensuremath{\infty}S\ensuremath→\ensuremath∞ limit to the deep quantum case S=1/2S=1/2S=1/2, including a transverse magnetic field. To this end, we combine different techniques such as classical energy minima, classical Monte Carlo, linear spin waves, bosonization, and density matrix renormalization group (DMRG). We find a phase transition from the already reported dipolar ferromagnetic region to an antiferromagnetic region for high enough antiferromagnetic exchange. Thermal and quantum fluctuations destabilize the classical order before reaching magnetic saturation in both phases, and also close to zero field in the antiferromagnetic phase. In the extreme quantum limit S=1/2S=1/2S=1/2, extensive DMRG computations show that the main phases remain present with transition lines to saturation significatively shifted to lower fields, in agreement with the bosonization analysis. The overall picture maintains a close analogy with the phase diagram of the anisotropic XXZ spin chain in a transverse field.
Hyperuniform states of matter are characterized by anomalous suppression of long-wavelength density fluctuations. While most of the interesting cases of disordered hyperuniformity are provided by complex many-body systems such as liquids or amorphous solids, classical spin chains with certain long-range interactions have been shown to demonstrate the same phenomenon. Such spin-chain systems are ideal models for exploring the effects of quantum mechanics on hyperuniformity. It is well-known that the transverse field Ising model shows a quantum phase transition (QPT) at zero temperature. Under the quantum effects of a transverse magnetic field, classical hyperuniform spin chains are expected to lose their hyperuniformity. High-precision simulations of these cases are complicated because of the presence of highly nontrivial long-range interactions. We perform an extensive analysis of these systems using density matrix renormalization group simulations to study the possibilities of phase transitions and the mechanism by which they lose hyperuniformity. Even for a spin chain of length 30, we see discontinuous changes in properties like the ``$\ensuremath{\tau}$ order metric'' of the ground state, the measure of hyperuniformity, and the second cumulant of the total magnetization along the xxx-direction, all suggestive of first-order QPTs. An interesting feature of the phase transitions in these disordered hyperuniform spin chains is that, depending on the parameter values, the presence of a transverse magnetic field may lead remarkably to an increase in the order of the ground state as measured by the ``$\ensuremath{\tau}$ order metric,'' even if hyperuniformity is lost. Therefore, it would be possible to design materials to target specific novel quantum behaviors in the presence of a transverse magnetic field. Our numerical investigations suggest that these spin chains can show no more than two QPTs. We further analyze the long-range interacting spin chains via the Jordan-Wigner mapping onto a system of spinless fermions, showing that under the pairwise-interaction approximation and a mean-field treatment, there can be at most two quantum phase transitions. Based on these numerical and theoretical explorations, we conjecture that for spin chains with long-range pair interactions that have convergent cosine transforms, there can be a maximum of two quantum phase transitions at zero temperature.
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We consider a long-range Ising antiferromagnet put in a transverse field (LRTIAF) with disorder. We have obtained the phase diagrams for both the classical and quantum cases. For the pure case applying quantum Monte Carlo method, we study the variation in order parameter (spin correlation in the Trotter direction), susceptibility, and average energy of the system for various values of the transverse field at different temperatures. The antiferromagnetic order is seen to get immediately broken as soon as the thermal or quantum fluctuations are added. We discuss generally the phase diagram for the same LRTIAF model with perturbative Sherrington-Kirkpatrick-type disorder. We find that while the antiferromagnetic order is immediately broken as one adds an infinitesimal transverse field or thermal fluctuation to the pure LRTIAF system, an infinitesimal SK spin-glass disorder is enough to induce a stable glass order in the LRTIAF. This glass order eventually gets destroyed as the thermal or quantum fluctuations are increased beyond their threshold values and the transition to paramagnetic phase occurs. Analytical studies for the phase transitions are discussed in details in each case. These transitions have been confirmed by applying classical and quantum Monte Carlo methods. We show here that the disordered LRTIAF has a surrogate incubation property of the SK spin glass phase.
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