Excitation spectrum gap and spin-wave velocity of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mi>X</mml:mi><mml:mi>Z</mml:mi></mml:mrow></mml:math>Heisenberg chains: Global renormalization-group calculation

Sarıyer, Ozan S.; Berker, A. Nihat; Hinczewski, Michael

doi:10.1103/physrevb.77.134413

Cited by 13 publications

(23 citation statements)

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“…J ij is equal to the ferromagnetic value of J > 0 with probability 1 − p and to the antiferromagnetic value of −J < 0 with probability p. We solve this model by extending the Suzuki-Takano rescaling [3,4,16,17,18,19,20,21,22,23,24] to non-uniform systems and to length-rescaling factor b = 3, necessary for the a priori equivalent treatment of ferromagnetism and antiferromagnetism, followed by the essentially exact treatment [25,26] of the quenched randomness giving the non-uniformity. In one dimension,…”

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confidence: 99%

Quantum-Mechanically Induced Asymmetry in the Phase Diagrams of Spin-Glass Systems

Kaplan

Berker

2008

Phys. Rev. Lett.

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The spin-1/2 quantum Heisenberg spin-glass system is studied in all spatial dimensions d by renormalization-group theory. Strongly asymmetric phase diagrams in temperature and antiferromagnetic bond probability p are obtained in dimensions d ≥ 3. The asymmetry at high temperatures approaching the pure ferromagnetic and antiferromagnetic systems disappears as d is increased. However, the asymmetry at low but finite temperatures remains in all dimensions, with the antiferromagnetic phase receding to the ferromagnetic phase. A finite-temperature second-order phase boundary directly between the ferromagnetic and antiferromagnetic phases occurs in d ≥ 6, resulting in a new multicritical point at its meeting with the boundaries to the paramagnetic phase. In d = 3, 4, 5, a paramagnetic phase reaching zero temperature intervenes asymmetrically between the ferromagnetic and reentrant antiferromagnetic phases. There is no spin-glass phase in any dimension.PACS numbers: 75.10. Nr, 64.60.Ak, 05.45.Df, 05.10.Cc A conspicuous finite-temperature effect of quantum mechanics is the critical temperature differentiation between ferromagnetic and antiferromagnetic systems. [1,2,3,4] This is a contrast to classical systems where, e.g., on loose-packed lattices ferromagnetic and antiferromagnetic systems are mapped onto each other and therefore have the same critical temperature. We find that this quantum effect is compounded and even more robust in spin-glass systems, which incorporate the passage from ferromagnetism and antiferromagnetism via quenched disorder.Thus, in the present work, the phase diagrams of the spin-1/2 quantum Heisenberg spin-glass systems are calculated in all dimensions d ≥ 3. In the space of temperature T and concentration p of antiferromagnetic bonds, remarkably asymmetric phase diagrams are obtained, in very strong contrast to the corresponding classical systems. Whereas, in the limit of d → ∞, the differentiation of the critical temperatures of the ferromagnetic and antiferromagnetic pure systems disappears, the T p phase diagrams remain strongly asymmetric at low but finite temperatures, where quantum fluctuations remain dominant independent of dimensionality. A direct second-order phase boundary between ferromagnetic and antiferromagnetic phases, also not seen in isotropic classical systems, is found in d > 5. In lower d, a paramagnetic phase intervenes between the ferromagnetic and antiferromagnetic systems. Our calculation is an approximation for hypercubic lattices and, simultaneously, a lesser approximation for hierarchical lattices [5,6,7,8,9,10,11,12,13,14,15].The spin-1/2 quantum Heisenberg spin-glass systems have the Hamiltonian −βH = ij J ij s i · s j ≡ ij −βH(i, j), where ij denotes a sum over pairs of nearest-neighbor sites. J ij is equal to the ferromagnetic value of J > 0 with probability 1 − p and to the antiferromagnetic value of −J < 0 with probability p. We solve this model by extending the Suzuki-Takano rescaling [3,4,16,17,18,19,20,21,22,23,24] to non-uniform systems and to length-re...

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confidence: 99%

Quantum-Mechanically Induced Asymmetry in the Phase Diagrams of Spin-Glass Systems

Kaplan

Berker

2008

Phys. Rev. Lett.

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“…Thus, as an approximation, the non-commutativity of the operators beyond three consecutive sites is ignored at each successive length scale, in the two steps indicated by ≃ in the above equation. Earlier studies [63][64][65][66][67][68][69][70][71][72][73][74] have established the quantitative validity of this procedure. The above transformation is algebraically summarized in…”

Section: Spinless Falicov-kimball Modelmentioning

confidence: 96%

Phase separation and charge-ordered phases of thed=3Falicov-Kimball model at nonzero temperature: Temperature-density-chemical potential global phase diagram from renormalization-group theory

2011

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The global phase diagram of the spinless Falicov-Kimball model in d = 3 spatial dimensions is obtained by renormalization-group theory. This global phase diagram exhibits five distinct phases. Four of these phases are charge-ordered (CO) phases, in which the system forms two sublattices with different electron densities. The CO phases occur at and near half filling of the conduction electrons for the entire range of localized electron densities. The phase boundaries are second order, except for the intermediate and large interaction regimes, where a first-order phase boundary occurs in the central region of the phase diagram, resulting in phase coexistence at and near half filling of both localized and conduction electrons. These two-phase or three-phase coexistence regions are between different charge-ordered phases, between charge-ordered and disordered phases, and between dense and dilute disordered phases. The second-order phase boundaries terminate on the first-order phase transitions via critical endpoints and double critical endpoints. The first-order phase boundary is delimited by critical points. The cross-sections of the global phase diagram with respect to the chemical potentials and densities of the localized and conduction electrons, at all representative interactions strengths, hopping strengths, and temperatures, are calculated and exhibit ten distinct topologies.

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“…where i, j, k are three successive sites in one-dimensional lattice, and βH ij is the dimensionless Hamiltonian operating on the ij-bond, such that the system Hamiltonian (3) reads βH = ij [βH ij ]. 48 In equation (5), the operator −β H ik acts on two-site states |s i ⊗ |s k of the renormalized system, while the operator −βH ij − βH jk acts on three-site states |s i ⊗ |s j ⊗ |s k of the original system.…”

Section: A Renormalization Group Transformation For D =mentioning

confidence: 99%

“…Hence, even at zero-temperature limit (J → ∞), results for thermodynamic functions obtained for b = 2 and d = 1, compare well with exact results. 48 On the anisotropy axis, the approximation becomes exact at the Ising limits, |∆| → ∞, where the operators become classical and commute with each other. Hence, we expect the worst results for the XY model (∆ = 0) at zero-temperature.…”

Section: A Renormalization Group Transformation For D =mentioning

confidence: 99%

“…46,47 Previously, we used the Suzuki-Takano approach to calculate thermodynamic functions of the XXZ model in d = 1 dimensions, and showed that the approximate RG procedure works well even in the low-temperature regime. 48 In this article, we study the model in d = 2 dimensions. We reproduce the results of Suzuki and Takano (phase diagram and critical properties), and ex-tend their work by calculating the thermodynamic functions globally at all temperatures and anisotropies.…”

Section: Introductionmentioning

confidence: 99%

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Two-dimensional quantum-spin-1/2 XXZ magnet in zero magnetic field: Global thermodynamics from renormalisation group theory

Sarıyer

2019

Philosophical Magazine

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Phase diagram, critical properties and thermodynamic functions of the two-dimensional field-free quantum-spin-1/2 XXZ model has been calculated globally using a numerical renormalization group theory. The nearest-neighbor spin-spin correlations and entanglement properties, as well as internal energy and specific heat are calculated globally at all temperatures for the whole range of exchange interaction anisotropy, from XY limit to Ising limits, for both antiferromagnetic and ferromagnetic cases. We show that there exists long-range (quasi-long-range) order at low-temperatures, and the low-lying excitations are gapped (gapless) in the Ising-like easy-axis (XY-like easy-plane) regime. Besides, we identify quantum phase transitions at zero-temperature.

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Excitation spectrum gap and spin-wave velocity ofXXZHeisenberg chains: Global renormalization-group calculation

Cited by 13 publications

References 46 publications

Quantum-Mechanically Induced Asymmetry in the Phase Diagrams of Spin-Glass Systems

Quantum-Mechanically Induced Asymmetry in the Phase Diagrams of Spin-Glass Systems

Phase separation and charge-ordered phases of thed=3Falicov-Kimball model at nonzero temperature: Temperature-density-chemical potential global phase diagram from renormalization-group theory

Two-dimensional quantum-spin-1/2 XXZ magnet in zero magnetic field: Global thermodynamics from renormalisation group theory

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