Quantum Monte Carlo simulation of S=1/2 Heisenberg model with four spin interaction

Tsukamoto, M.; Harada, Kenji; Kawashima, Naoki

doi:10.1088/1742-6596/150/4/042218

Cited by 3 publications

(5 citation statements)

References 10 publications

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“…In such models, the critical exponent, η, always satisfies the condition η = 1/4. However, the observed exponent η ∼ 0.59 of the SU(2) JQ 2 model differs from the expected value [15]. In the SU(2) JQ 2 model, the VBS order is very weak because the QPT point is located in the vicinity of the limit, and the model can only be ex-pressed using the multibody interacting Q m term (the dimer limit).…”

Section: Introductionmentioning

confidence: 68%

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Thermal phase transition of generalized Heisenberg models forSU(N)spins on square and honeycomb lattices

et al. 2015

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We investigate thermal phase transitions to a valence-bond solid phase in SU(N) Heisenberg models with four-or six-body interactions on a square or honeycomb lattice, respectively. In both cases, a thermal phase transition occurs that is accompanied by rotational symmetry breaking of the lattice. We perform quantum Monte Carlo calculations in order to clarify the critical properties of the models. The estimated critical exponents indicate that the universality classes of the squareand honeycomb-lattice cases are identical to those of the classical XY model with a Z4 symmetrybreaking field and the 3-state Potts model, respectively. In the square-lattice case, the thermal exponent, ν, monotonically increases as the system approaches the quantum critical point, while the values of the critical exponents, η and γ/ν, remain constant. From a finite-size scaling analysis, we find that the system exhibits weak universality, because the Z4 symmetry-breaking field is always marginal. In contrast, ν in the honeycomb-lattice case exhibits a constant value, even in the vicinity of the quantum critical point, because the Z3 field remains relevant in the SU(3) and SU(4) cases.

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Section: Introductionmentioning

confidence: 68%

“…The universality class of the thermal transition has been discussed for both SU(2) JQ 2 [15] and JQ 3 [16] models on the square lattice. The VBS pattern on the square lattice is described by a columnar dimer configuration, which is characterized by the spontaneous breaking of π/2-rotational symmetry around the center of the plaquette.…”

Section: Introductionmentioning

confidence: 99%

Thermal phase transition of generalized Heisenberg models forSU(N)spins on square and honeycomb lattices

et al. 2015

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“…Instead, at the lowest T c reached here, ν ≈ 3. We expect that the same behavior should apply also in the J-Q 2 model, but that cross-over behaviors associated with the proximity to the quantumcritical point for all Q 2 /J in that model may make it difficult to extract the exponents there [34]. The significance of establishing the nature of the T > 0 critical line is that it puts the phase diagram of the J-Q model firmly within an established CFT.…”

Section: (A)mentioning

confidence: 89%

“…The T > 0 VBS transition was previously studied by Tsukamoto, Harada and Kawashima [34], who carried out QMC simulations of the J-Q 2 version of the J-Q model, where the Q 2 interaction is one of products of two singlet projectors. The results were puzzling, with significant deviations from the "weak universality" scenario applying to the transitions discussed above, where the critical correlation-function exponent η = 1/4 is constant (while other exponents depend on system details).…”

mentioning

confidence: 99%

“…The results were puzzling, with significant deviations from the "weak universality" scenario applying to the transitions discussed above, where the critical correlation-function exponent η = 1/4 is constant (while other exponents depend on system details). Instead, η ≈ 0.5 was obtained [34]. Here we consider the J-Q 3 model [12], where the Q 3 term consists of three bond-singlet projectors (forming columns on three adjacent lattuce links).…”

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confidence: 99%

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Thermal valence-bond-solid transition of quantum spins in two dimensions

Jin

Sandvik

2013

Phys. Rev. B

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We study the S=1/2 Heisenberg (J) model on the two-dimensional square lattice in the presence of additional higher-order spin interactions (Q) which lead to a valence-bond-solid (VBS) ground state. Using quantum Monte Carlo simulations, we analyze the thermal VBS transition. We find continuously varying exponents, with the correlation-length exponent "nu" close to the Ising value for large Q/J and diverging when Q/J approaches the quantum-critical point (the critical temperature Tc -> 0). This is in accord with the theory of deconfined quantum-critical points, which predicts that the transition should approach a Kosterlitz-Thouless (KT) fixed point when Tc -> 0+ (while the transition versus Q/J for T=0 is in a different class). We find explicit evidence for KT physics by studying the emergence of U(1) symmetry of the order parameter at T=T_c when Tc -> 0.Comment: 5 pages, 5 figure

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Ashkin-Teller Criticality and Pseudo-First-Order Behavior in a Frustrated Ising Model on the Square Lattice

2012

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We study the challenging thermal phase transition to stripe order in the frustrated square-lattice Ising model with couplings J(1) < 0 (nearest-neighbor, ferromagnetic) and J(2) > 0 (second-neighbor, antiferromagnetic) for g = J(2)/|J(1| > 1/2. Using Monte Carlo simulations and known analytical results, we demonstrate Ashkin-Teller criticality for g ≥ g*; i.e., the critical exponents vary continuously between those of the 4-state Potts model at g = g* and the Ising model for g → ∞. Thus, stripe transitions offer a route to realizing a related class of conformal field theories with conformal charge c = 1 and varying exponents. The transition is first order for g < g* = 0.67 ± 0.01, much lower than previously believed, and exhibits pseudo-first-order behavior for |g* ≤ g

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Quantum Monte Carlo simulation of S=1/2 Heisenberg model with four spin interaction

Cited by 3 publications

References 10 publications

Thermal phase transition of generalized Heisenberg models forSU(N)spins on square and honeycomb lattices

Thermal phase transition of generalized Heisenberg models forSU(N)spins on square and honeycomb lattices

Thermal valence-bond-solid transition of quantum spins in two dimensions

Ashkin-Teller Criticality and Pseudo-First-Order Behavior in a Frustrated Ising Model on the Square Lattice

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