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Physical review. B./Physical review. B

Prediction of the existence of a spin-liquid-like phase in the antiferromagnetic J1−J2 spin-12 system on the body-centered cubic lattice

E. Jurčišinová, Marian Jurčisin

Published Jun 29, 2020• 11 citations
Publisher

Abstract

The phase transitions and thermodynamics of the antiferromagnetic system with the presence of the next-to-nearest-neighbor interaction on the body-centered cubic lattice are studied within an exactly solvable model using the recursive lattice approach. It is shown that, besides the N\'eel and collinear antiferromagnetic phases and the paramagnetic phase discussed in the literature, the model clearly exhibits the existence of an intermediate phase that separates the antiferromagnetic phases. This new phase is observed in a narrow interval of the frustration parameter for nonzero temperatures and is realized in the form of a discrete (single-point-like) ground state in the zero-temperature limit. Transitions between all model phases are studied and it is shown that all transitions between each antiferromagnetic phase of the model and the paramagnetic one as well as between the antiferromagnetic phases and the intermediate phase have the second-order phase transition nature. The magnetization, entropy, and specific heat capacity properties of all phases of the model are studied in detail. Three different ground states are identified and their macroscopic degeneracies are determined. The anomalous Schottky-type behavior of the specific heat capacity in the vicinity of the highly macroscopically degenerated ground state realized for exactly given value of the frustration parameter is observed and discussed. Besides, the existence of the intermediate phase leads to the nontrivial temperature behavior of the specific heat capacity where, in addition to the Schottky-type anomaly related to the frustration, three discontinuous jumps related to the three consecutive second-order phase transitions between corresponding model phases are observed.

DOI
10.1103/physrevb.101.214443

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Quantum phase transition in the three-dimensional anisotropic frustrated Heisenberg antiferromagnetic model

J. Roberto Viana, J. Ricardo de Sousa, M. A. Contínentino

The phase diagram of the anisotropic quantum spin-1/2 Heisenberg antiferromagnet in the presence of competitive nearest $({J}_{1})$- and next-nearest $({J}_{2}=\ensuremath{\alpha}{J}_{1})$-neighbor interactions on a simple cubic lattice is studied within the framework of the differential operator technique. The Hamiltonian is solved by using an effective-field theory in a two-spin cluster. We propose a function for the free energy, which is similar to the Landau expansion, in order to find the ground state $(T=0)$ and the finite-$T$ phase diagram. At zero temperature, we find a first-order quantum phase transition in the point ${\ensuremath{\alpha}}_{c}(\ensuremath{\Delta})$ between the antiferromagnetic (AF) and superantiferromagnetic (SAF) phases. This is dependent on the anisotropy parameter $\ensuremath{\Delta}$ ($\ensuremath{\Delta}=0$ and 1 correspond to the isotropic Heisenberg and Ising models, respectively). The quantum critical values of ${\ensuremath{\alpha}}_{c}(\ensuremath{\Delta}\ensuremath{\ne}1)={\ensuremath{\alpha}}_{c}^{q}(\ensuremath{\Delta})$ are smaller than those of the classical model ${\ensuremath{\alpha}}_{c}(\ensuremath{\Delta}=1)={\ensuremath{\alpha}}_{c}^{c}=1/4$ (for example, for $\ensuremath{\Delta}=0$, we find ${\ensuremath{\alpha}}_{c}^{q}(0)=0.21$). The former monotonically increases with the anisotropy parameter $\ensuremath{\Delta}$. The phase diagram in $T\text{\ensuremath{-}}\ensuremath{\alpha}$ plane presents a second-order transition at ${T}_{2}(\ensuremath{\alpha})$ between the AF and paramagnetic (P) phases. The phase transition between the SAF and P phases is of first-order ${T}_{1}(\ensuremath{\alpha})$ for all values of $\ensuremath{\Delta}∊[0,1]$. The phase transition lines ${T}_{1}(\ensuremath{\alpha})$ and ${T}_{2}(\ensuremath{\alpha})$ merge in a critical end point (CEP) that is dependent on $\ensuremath{\Delta}$ [i.e., ${T}_{\text{CEP}}(\ensuremath{\Delta})$ and ${\ensuremath{\alpha}}_{\text{CEP}}(\ensuremath{\Delta})$ are the temperature and frustration parameters at the CEP]. The ordered phases (AF and SAF) are separated by first-order transitions and exhibit a nontrivial re-entrant behavior at low temperatures.

Physical Review B•May 27, 2008•24 citations
The phase transitions and thermodynamics of the antiferromagnetic system with the presence of the next-to-nearest-neighbor interaction on the body-centered cubic lattice are studied within an exactly solvable model using the recursive lattice approach. It is shown that, besides the N'eel and collinear antiferromagnetic phases and the paramagnetic phase discussed in the literature, the model clearly exhibits the existence of an intermediate phase that separates the antiferromagnetic phases. This new phase is observed in a narrow interval of the frustration parameter for nonzero temperatures and is realized in the form of a discrete (single-point-like) ground state in the zero-temperature limit. Transitions between all model phases are studied and it is shown that all transitions between each antiferromagnetic phase of the model and the paramagnetic one as well as between the antiferromagnetic phases and the intermediate phase have the second-order phase transition nature. The magnetization, entropy, and specific heat capacity properties of all phases of the model are studied in detail. Three different ground states are identified and their macroscopic degeneracies are determined. The anomalous Schottky-type behavior of the specific heat capacity in the vicinity of the highly macroscopically degenerated ground state realized for exactly given value of the frustration parameter is observed and discussed. Besides, the existence of the intermediate phase leads to the nontrivial temperature behavior of the specific heat capacity where, in addition to the Schottky-type anomaly related to the frustration, three discontinuous jumps related to the three consecutive second-order phase transitions between corresponding model phases are observed.
The ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model is a ``canonical'' model in the field of quantum magnetism in order to study the interplay between frustration and quantum fluctuations as well as quantum phase transitions driven by frustration. Here we apply the coupled cluster method (CCM) to study the spin-half ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model with antiferromagnetic nearest-neighbor bonds J1>0{J}_{1}>0J1​>0 and next-nearest-neighbor bonds J2>0{J}_{2}>0J2​>0 for the simple cubic (sc) and body-centered cubic (bcc) lattices. In particular, we wish to study the ground-state ordering of these systems as a function of the frustration parameter p=z2J2/z1J1p={z}_{2}{J}_{2}/{z}_{1}{J}_{1}p=z2​J2​/z1​J1​, where z1(z2){z}_{1} ({z}_{2})z1​(z2​) is the number of nearest (next-nearest) neighbors. We wish to determine the positions of the phase transitions using the CCM and we aim to resolve the nature of the phase transition points. We consider the ground-state energy, order parameters, spin-spin correlation functions, as well as the spin stiffness in order to determine the ground-state phase diagrams of these models. We find a direct first-order phase transition at a value of p=0.528p=0.528p=0.528 from a state of nearest-neighbor N\'eel order to next-nearest-neighbor N\'eel order for the bcc lattice. For the sc lattice the situation is more subtle. CCM results for the energy, the order parameter, the spin-spin correlation functions, and the spin stiffness indicate that there is no direct first-order transition between ground-state phases with magnetic long-range order, rather it is more likely that two phases with antiferromagnetic long range are separated by a narrow region of a spin-liquid-like quantum phase around p=0.55p=0.55p=0.55. Thus the strong frustration present in the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the sc lattice may open a window for an unconventional quantum ground state in this three-dimensional spin model.
Ground-state phases of S=1/2S = 1/2S=1/2 Heisenberg models on the body-centered cubic lattice
Simulating low-temperature properties of three-dimensional frustrated quantum magnets is challenging due to the sign problem and the system sizes required to mitigate substantial finite-size effects. However, there are many experimental examples of three-dimensional crystals that could host exotic low-temperature states of matter, such as quantum spin liquids. We calculate the ground-state phase diagrams of frustrated quantum spin models on the body-centered cubic lattice using neural quantum states. First, we study the antiferromagnetic J1−J2J_1-J_2J1​−J2​ model where we find a direct first-order phase transition between Néel and collinear long-range-ordered phases at (J2/J1)c=0.705(J_2/J_1)_c = 0.705(J2​/J1​)c​=0.705, consistent with previous studies. Then, in a tetragonally-distorted variant, proposed as a minimal model of NaCa2_22​Cu2_22​(VO4_44​)3_33​, we find no evidence of a quantum paramagnetic ground state, with a first-order phase transition between Néel and chain phases at (J2ab/J1)c=1.0375(J_{2ab}/J_1)_c = 1.0375(J2ab​/J1​)c​=1.0375. Therefore, the ground state of the tetragonally-distorted model does not reproduce the low-temperature magnetic properties of NaCa2_22​Cu2_22​(VO4_44​)3_33​, and the inclusion of other effects is necessary to rationalize experimental observations.
We have studied phase transitions and thermodynamic properties of the antiferromagnetic Potts model with number of spin states q = 3 on a body-centered cubic lattice by the Monte Carlo method. Investigations have been performed with account for exchange interactions J1 and J2 between the first and second nearest neighbors. The phase transition order has been analyzed using the histogram method. It is found that in this model with J2 = 0, a second-order phase transition is observed. It is concluded that the inclusion of the interaction between the second nearest neighbors changes the type of the phase transition.
Abstract The Monte Carlo method has been used to study phase transitions and critical properties of the antiferromagnetic 3-state Potts model on a body-centered cubic lattice with interactions of the first (J1) and second (J2) nearest neighbors. The competition of exchange interactions in the range –2/3 < J2 < 0 was determined to result in a phase separation. In the low-temperature region, an ordered phase, lying inside the phase with broken sublattice symmetry, was found. The magnetic structures of the ground state corresponding to different regions of the phase diagram have been obtained. The analysis of the phase transition order has been carried out using the Binder cumulant method and the histogram method. It has been revealed that the interaction of the second nearest neighbors leads to a change in the type of phase transition. Static critical exponents have been calculated based on scaling relations. The critical exponents correspond to the universality class of the three-dimensional XY model.
Abstract We have studied phase transitions and thermodynamic properties of the antiferromagnetic Potts model with number of spin states q = 3 on a body-centered cubic lattice by the Monte Carlo method. Investigations have been performed with account for exchange interactions J1 and J2 between the first and second nearest neighbors. The phase transition order has been analyzed using the histogram method. It is found that in this model with J2 = 0, a second-order phase transition is observed. It is concluded that the inclusion of the interaction between the second nearest neighbors changes the type of the phase transition.
The phase diagram of the anisotropic quantum spin-1/2 Heisenberg antiferromagnet in the presence of competitive nearest (J1)({J}_{1})(J1​)- and next-nearest $({J}_{2}=\ensuremath{\alpha}{J}_{1})$-neighbor interactions on a simple cubic lattice is studied within the framework of the differential operator technique. The Hamiltonian is solved by using an effective-field theory in a two-spin cluster. We propose a function for the free energy, which is similar to the Landau expansion, in order to find the ground state (T=0)(T=0)(T=0) and the finite-TTT phase diagram. At zero temperature, we find a first-order quantum phase transition in the point ${\ensuremath{\alpha}}_{c}(\ensuremath{\Delta})$ between the antiferromagnetic (AF) and superantiferromagnetic (SAF) phases. This is dependent on the anisotropy parameter $\ensuremath{\Delta}$ ($\ensuremath{\Delta}=0$ and 1 correspond to the isotropic Heisenberg and Ising models, respectively). The quantum critical values of ${\ensuremath{\alpha}}_{c}(\ensuremath{\Delta}\ensuremath{\ne}1)={\ensuremath{\alpha}}_{c}^{q}(\ensuremath{\Delta})$ are smaller than those of the classical model ${\ensuremath{\alpha}}_{c}(\ensuremath{\Delta}=1)={\ensuremath{\alpha}}_{c}^{c}=1/4$ (for example, for $\ensuremath{\Delta}=0$, we find ${\ensuremath{\alpha}}_{c}^{q}(0)=0.21$). The former monotonically increases with the anisotropy parameter $\ensuremath{\Delta}$. The phase diagram in $T\text{\ensuremath{-}}\ensuremath{\alpha}$ plane presents a second-order transition at ${T}_{2}(\ensuremath{\alpha})$ between the AF and paramagnetic (P) phases. The phase transition between the SAF and P phases is of first-order ${T}_{1}(\ensuremath{\alpha})$ for all values of $\ensuremath{\Delta}∊[0,1]$. The phase transition lines ${T}_{1}(\ensuremath{\alpha})$ and ${T}_{2}(\ensuremath{\alpha})$ merge in a critical end point (CEP) that is dependent on $\ensuremath{\Delta}$ [i.e., ${T}_{\text{CEP}}(\ensuremath{\Delta})$ and ${\ensuremath{\alpha}}_{\text{CEP}}(\ensuremath{\Delta})$ are the temperature and frustration parameters at the CEP]. The ordered phases (AF and SAF) are separated by first-order transitions and exhibit a nontrivial re-entrant behavior at low temperatures.