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Physical review. B./Physical review. B

Phase transitions in the spin- 1 2 Heisenberg antiferromagnet on the dimerized diamond lattice

Ronja Bärwolf, Alexander Sushchyev, Francesco Parisen Toldin, Stefan Weßel

Published Feb 19, 2025• 2 citations
Publisher

Abstract

Using a combination of unbiased quantum Monte Carlo simulations and a decoupled dimer mean-field theory, we investigate the thermal and quantum phase transitions of the spin- 1 2 Heisenberg model on the dimerized diamond lattice. We find that at sufficiently strong dimerization the system exhibits a quantum disordered ground state, in contrast to the antiferromagnetic phase stabilized at weak dimerization. We determine the quantum critical point and examine the thermodynamic responses in both regimes. The ratio for the critical interdimer ( J c ) to intradimer ( J D ) coupling is obtained as J c / J D = 0.3615 ( 5 ) . Our results show that the decoupled dimer mean-field theory well captures the competition between the local singlet formation and the antiferromagnetic ordering tendency, and thus provides an appropriate qualitative description of this three-dimensional quantum magnet, in contrast to the conventional mean-field decoupling. We also examine the differences in the ordering temperatures between the antiferromagnetic and the ferromagnetic spin- 1 2 Heisenberg model on the diamond lattice based on quantum Monte Carlo simulations.

DOI
10.1103/physrevb.111.085136

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Using a combination of unbiased quantum Monte Carlo simulations and a decoupled dimer mean-field theory, we investigate the thermal and quantum phase transitions of the spin- 1 2 Heisenberg model on the dimerized diamond lattice. We find that at sufficiently strong dimerization the system exhibits a quantum disordered ground state, in contrast to the antiferromagnetic phase stabilized at weak dimerization. We determine the quantum critical point and examine the thermodynamic responses in both regimes. The ratio for the critical interdimer ( J c ) to intradimer ( J D ) coupling is obtained as J c / J D = 0.3615 ( 5 ) . Our results show that the decoupled dimer mean-field theory well captures the competition between the local singlet formation and the antiferromagnetic ordering tendency, and thus provides an appropriate qualitative description of this three-dimensional quantum magnet, in contrast to the conventional mean-field decoupling. We also examine the differences in the ordering temperatures between the antiferromagnetic and the ferromagnetic spin- 1 2 Heisenberg model on the diamond lattice based on quantum Monte Carlo simulations.
Using a combination of unbiased quantum Monte Carlo simulations and a decoupled dimer mean-field theory, we investigate the thermal and quantum phase transitions of the spin-1/2 Heisenberg model on the dimerized diamond lattice. We find that at sufficiently strong dimerization the system exhibits a quantum disordered ground state, in contrast to the antiferromagnetic phase stabilized at weak dimerization. We determine the quantum critical point and examine the thermodynamic responses in both regimes. The ratio for the critical interdimer (JcJ_cJc​) to intradimer (JDJ_DJD​) coupling is obtained as Jc/JD=0.3615(5)J_c/J_D = 0.3615(5)Jc​/JD​=0.3615(5). Our results show that the decoupled dimer mean-field theory well captures the competition between the local singlet formation and the antiferromagnetic ordering tendency, and thus provides an appropriate qualitative description of this three-dimensional quantum magnet, in contrast to the conventional mean-field decoupling. We also examine the differences in the ordering temperatures between the antiferromagnetic and the ferromagnetic spin-1/2 Heisenberg model on the diamond lattice based on quantum Monte Carlo simulations.
We use quantum Monte Carlo simulations to study effects of disorder on the quantum phase transition occurring versus the ratio $g=J/{J}^{\ensuremath{'}}$ in square-lattice dimerized S=1/2S=1/2S=1/2 Heisenberg antiferromagnets with intradimer and interdimer couplings JJJ and ${J}^{\ensuremath{'}}$. The dimers are either randomly distributed (as in the classical dimer model), or come in parallel pairs with horizontal or vertical orientation. In both cases the transition violates the Harris criterion, according to which the correlation-length exponent should satisfy $\ensuremath{\nu}\ensuremath{\ge}1$. We do not detect any deviations from the three-dimensional O(3) universality class obtaining in the absence of disorder (where $\ensuremath{\nu}\ensuremath{\approx}0.71$). We discuss special circumstances which allow $\ensuremath{\nu}<1$ for the type of disorder considered here.
The spin-1/2 Heisenberg antiferromagnet on the frustrated diamond-decorated square lattice is known to feature various zero-field ground-state phases, consisting of extended monomer-dimer and dimer-tetramer ground states as well as a ferrimagnetic regime. Using a combination of analytical arguments, density matrix renormalization group (DMRG), exact diagonalization as well as sign-problem-free quantum Monte Carlo (QMC) calculations, we investigate the properties of this system and the related Lieb lattice in the presence of a finite magnetic field, addressing both the ground-state phase diagram as well as several thermodynamic properties. In addition to the zero-field ground states, we find at high magnetic field a spin-canted phase with a continuously rising magnetization for increasing magnetic field strength as well as the fully polarized paramagnetic phase. At intermediate field strength, we identify a first-order quantum phase transition line between the ferrimagnetic and the monomer-dimer regime. This first-order line extends to finite temperatures, terminating in a line of critical points that belong to the universality class of the two-dimensional Ising model.
The spin-1/2 Heisenberg antiferromagnet on the diamond-decorated square lattice in the presence of a magnetic field displays various quantum phases including the Lieb-Mattis ferrimagnetic, dimer-tetramer, monomer-dimer, and spin-canted phases, in addition to the trivial fully saturated state. Thermodynamic properties of this model are investigated using several complementary analytical and numerical methods such as exact diagonalization up to the systems of 40 spins, an effective monomer-dimer description, sign-problem-free quantum Monte Carlo simulations for up to 180 spins, and a decoupling approximation. Our particular attention is focused on the parameter region favoring the dimer-tetramer phase. This ground state can be represented by a classical hard-dimer model on the square lattice and retains a macroscopic degeneracy even under a magnetic field. However, the description of the low-temperature thermodynamics close to the boundary between the macroscopically degenerate dimer-tetramer and the nondegenerate monomer-dimer phases requires an extended classical monomer-dimer lattice-gas model. Anomalous thermodynamic properties emerging in the vicinity of the dimer-tetramer phase are studied in detail. Under the adiabatic demagnetization we detect an enhanced magnetocaloric effect promoting an efficient cooling to absolute zero temperature.
Using large-scale quantum Monte Carlo simulations, we determine the ground state phase diagram of the spin-1/2 antiferromagnetic Heisenberg model on the honeycomb lattice for the most generic case of three varying interaction strengths along the different lattice directions. We identify continuous quantum phase transition lines that separate the long-range ordered antiferromagnetic regime from three distinct quantum-disordered phases, each characterized by dominant dimer-singlet formations. The finite-size behavior along these phase transition lines exhibits anomalously large corrections to scaling, which we relate to similar recent findings in certain dimerized quantum spin systems and to singular one-dimensional limits in the model parameter space. We also comment more generally on the nonuniversality of critical cumulant ratios in anisotropic systems and attempts to restore universality by varying the aspect ratio.
Using a combination of quantum Monte Carlo simulations in adapted cluster bases, the finite-temperature Lanczos method, and an effective Hamiltonian approach, we explore the thermodynamic properties of the spin-1/2 Heisenberg antiferromagnet on the star lattice. We consider various parameter regimes on this strongly frustrated Archimedean lattice, including the case of homogeneous couplings as well as the distinct parameter regimes of dominant vs weak dimer coupling. For the latter case, we explore the quantum phase diagram in the presence of inhomogeneous trimer couplings, preserving inversion symmetry. We compare the efficiency of different cluster decoupling schemes for the quantum Monte Carlo simulations in terms of the sign problem, contrast the thermodynamic properties to those of other strongly frustrated quantum magnets such as the kagome lattice model, and comment on previous results from tensor-network calculations regarding a valence bond crystal phase in the regime of weak dimer coupling. Finally, we relate our results to recently reported experimental findings on a Cu-based quantum magnetic spin-1/2 compound with an underlying star lattice structure.