Rigorous results on a first-order phase transition in antiferromagnetic spin-1/2 coupled chains

Xian, Yang

doi:10.1103/physrevb.52.12485

Cited by 70 publications

(97 citation statements)

References 25 publications

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“…Like the Shastry-Sutherland model, it exhibits a phase with a dimer-singlet ground state, fully localized triplet excitations, and a first-order phase transition [47,49]. The importance of multi-triplet bound-state excitations was also recognized in early analytical studies of the fully frustrated ladder [47,49] and observed in a DMRG calculation [52].…”

Section: Introductionmentioning

confidence: 97%

“…the model of Eq. (1) with J × = J ] possesses a first-order quantum phase transition as a function of the coupling ratio J ⊥ /J [49,53]. This transition separates a rung-singlet phase for strong J ⊥ from a rung-triplet, or Haldane [3], phase at weak J ⊥ .…”

Section: Ground Statementioning

confidence: 99%

“…1. A significant amount of information is already available concerning the zero-temperature properties of this precise model [47][48][49][50][51][52][53][54] and variants thereof [55][56][57][58][59][60][61][62]. Like the Shastry-Sutherland model, it exhibits a phase with a dimer-singlet ground state, fully localized triplet excitations, and a first-order phase transition [47,49].…”

Section: Introductionmentioning

confidence: 99%

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Thermodynamic properties of highly frustrated quantum spin ladders: Influence of many-particle bound states

et al. 2016

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Quantum antiferromagnets have proven to be some of the cleanest realizations available for theoretical, numerical, and experimental studies of quantum fluctuation effects. At finite temperatures, however, the additional effects of thermal fluctuations in the restricted phase space of a low-dimensional system have received much less attention, particularly the situation in frustrated quantum magnets, where the excitations may be complex collective (bound or even fractionalized) modes. We investigate this problem by studying the thermodynamic properties of the frustrated two-leg S = 1/2 spin ladder, with particular emphasis on the fully frustrated case. We present numerical results for the magnetic specific heat and susceptibility, obtained from exact diagonalization and quantum Monte Carlo studies, which we show can be rendered free of the sign problem even in a strongly frustrated system and which allow us to reach unprecedented sizes of L = 200 ladder rungs. We find that frustration effects cause an unconventional evolution of the thermodynamic response across the full parameter regime of the model. However, close to the first-order transition they cause a highly anomalous reduction in temperature scales with no concomitant changes in the gap; the specific heat shows a very narrow peak at very low energies and the susceptibility rises abruptly at extremely low temperatures. Unusually, the two quantities have different gaps over an extended region of the parameter space. We demonstrate that these results reflect the presence of large numbers of multi-particle bound-state excitations, whose energies fall below the one-triplon gap in the transition region.

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Section: Introductionmentioning

confidence: 97%

Section: Ground Statementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Thermodynamic properties of highly frustrated quantum spin ladders: Influence of many-particle bound states

et al. 2016

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“…On the other hand, there are cases in which frustration causes a first-order transition in quantum spin systems in contrast to a second-order transition in the corresponding classical model (see for example Refs. [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Quantum phase transitions of a square-lattice Heisenberg antiferromagnet with two kinds of nearest-neighbor bonds: A high-order coupled-cluster treatment

Krüger¹,

Richter²,

Schulenburg³

et al. 2000

Phys. Rev. B

105

272

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We study the zero-temperature phase diagram and the low-lying excitations of a square-lattice spinhalf Heisenberg antiferromagnet with two types of regularly distributed nearest-neighbour exchange bonds (J > 0 (antiferromagnetic) and −∞ < J ′ < ∞) using the coupled cluster method (CCM) for high orders of approximation (up to LSUB8). We use a Néel model state as well as a helical model state as a starting point for the CCM calculations. We find a second-order transition from a phase with Néel order to a finite-gap quantum disordered phase for sufficiently large antiferromagnetic exchange constants J ′ > 0. For frustrating ferromagnetic couplings J ′ < 0 we find indications that quantum fluctuations favour a first-order phase transition from the Néel order to a quantum helical state, by contrast with the corresponding second-order transition in the corresponding classical model. The results are compared to those of exact diagonalizations of finite systems (up to 32 sites) and those of spin-wave and variational calculations. The CCM results agree well with the exact diagonalization data over the whole range of the parameters. The special case of J ′ = 0, which is equivalent to the honeycomb lattice, is treated more closely.

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“…The entire region below the transition line is in the Haldane phase, being continuously related to the point (J × /J = 1, J ⊥ /J = 0) at which the ladder is equivalent to a spin-1 chain. [3][4][5][6][7] The debate centred over the existence or not of a columnar dimer (CD) phase intermediate between the rung-singlet and Haldane phases which was predicted on the basis of weak coupling field theory renormalisation group arguments. 17 This phase is between…”

Section: Introductionmentioning

confidence: 99%

The antiferromagnetic cross-coupled spin ladder: Quantum fidelity and tensor networks approach

Chen

Cho

Zhou

et al. 2016

Journal of the Korean Physical Society

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We investigate the phase diagram of the cross-coupled Heisenberg spin ladder with antiferromagnetic couplings. For this model there have been conflicting results for the existence of the columnar dimer phase, which was predicted on the basis of weak coupling field theory renormalisation group arguments. The numerical work on this model has been based on various approaches, including exact diagonalization, series expansions and density-matrix renormalization group calculations. Using the recently developed tensor network states and ground-state fidelity approach for quantum spin ladders we find no evidence for the existence of the columnar dimer phase. We also provide an argument based on the symmetry of the Hamiltonian which suggests that the phase diagram for antiferromagnetic couplings consists of a single line separating the rung-singlet and Haldane phases.

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Rigorous results on a first-order phase transition in antiferromagnetic spin-1/2 coupled chains

Cited by 70 publications

References 25 publications

Thermodynamic properties of highly frustrated quantum spin ladders: Influence of many-particle bound states

Thermodynamic properties of highly frustrated quantum spin ladders: Influence of many-particle bound states

Quantum phase transitions of a square-lattice Heisenberg antiferromagnet with two kinds of nearest-neighbor bonds: A high-order coupled-cluster treatment

The antiferromagnetic cross-coupled spin ladder: Quantum fidelity and tensor networks approach

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