Antiferromagnetic model with known ground state

Majumdar, Chanchal K.

doi:10.1088/0022-3719/3/4/019

Cited by 250 publications

(173 citation statements)

References 13 publications

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“…Only one fixed point (J ⊥ = J z and J ′ = J z /2) is known to possess an analytic ground state 14 . In the rest of the phase diagram, the model (2.1) seems not to be integrable 15,16 .…”

Section: Definitions and Methodsmentioning

confidence: 99%

Nonergodic dynamics of the extended anisotropic Heisenberg chain

2006

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The issue of ergodicity is often underestimated. The presence of zero-frequency excitations in bosonic Green's functions determine the appearance of zero-frequency momentum-dependent quantities in correlation functions. The implicit dependence of matrix elements make such quantities also relevant in the computation of susceptibilities. Consequently, the correct determination of these quantities is of great relevance and the well-established practice of fixing them by assuming the ergodicity of the dynamics is quite questionable as it is not justifiable a priori by no means. In this manuscript, we have investigated the ergodicity of the dynamics of the z-component of the spin in the 1D Heisenberg model with anisotropic nearest-neighbor and isotropic next-nearest-neighbor interactions. We have obtained the zero-temperature phase diagram in the thermodynamic limit by extrapolating Exact and Lanczos diagonalization results computed on chains with sizes L = 6 ÷ 26. Two distinct non-ergodic regions have been found: one for J ′ /Jz 0.3 and |J ⊥ |/Jz < 1 and another for J ′ /Jz 0.25 and |J ⊥ |/Jz = 1. On the contrary, finite-size scaling of T = 0 results, obtained by means of Exact diagonalization on chains with sizes L = 4 ÷ 18, indicates an ergodic behavior of dynamics in the whole range of parameters.

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Section: Definitions and Methodsmentioning

confidence: 99%

Nonergodic dynamics of the extended anisotropic Heisenberg chain

2006

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“…Such a phase is characterized by a finite gap in the low lying excitation spectrum. The Majumdar-Ghosh model (Majumdar, 1970;Majumdar and Ghosh, 1969a,b) is obtained from Eq. (26) for α = 1/2.…”

Section: Frustrated Spin-1/2 Modelsmentioning

confidence: 99%

Entanglement in many-body systems

Amico¹,

et al. 2008

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The recent interest in aspects common to quantum information and condensed matter has prompted a flory of activity at the border of these disciplines that were far distant untill few years ago. Numerous interesting questions have been addressed so far. Here we review an important part of this field, the properties of the entanglement in many-body systems. We discuss the zero and finite temperature properties of entanglement in interacting spin, fermion and boson model systems. Both bipartite and multipartite entanglement will be considered. In equilibrium we show how entanglement is tightly connected to the characteristics of the phase diagram. The behavior of entanglement can be related, via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an experimental test. Out of equilibrium we discuss how to generate and manipulate entangled states by means of many-body Hamiltonians.

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“…WhenJ NNN ≡ J NNN /J 1 = 0.5, the ground state of the NNN interaction model is an array of independent singlet dimers, where the translational symmetry by one spin spacing is spontaneously broken [7,8]. Then there should exist the critical point of the ground-state phase transition between the spin-fluid (SF) state and the dimer state.…”

Section: Analytical and Physical Approachmentioning

confidence: 99%

The ground state of anS= 1/2 distorted diamond chain - a model of Cu₃Cl₆(H₂O)₂·2H₈C₄SO₂

Okamoto¹,

Tonegawa²,

Takahashi³

et al. 1999

J. Phys.: Condens. Matter

110

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We study the ground state of the model Hamiltonian of the trimerized S = 1/2 quantum Heisenberg chain Cu3Cl6(H2O)22H8C4SO2 in which a non-magnetic ground state was observed recently. This model consists of stacked trimers and has three kinds of coupling constant describing the couplings between spins: the intra-trimer coupling constant J1 and the inter-trimer coupling constants J2 and J3. All of these constants are assumed to be antiferromagnetic. By use of an analytical method and physical considerations, we show that there are three phases on the 2 - 3 plane (2J2 / J1, 3J3 / J1): the dimer phase, the spin-fluid phase and the ferrimagnetic phase. The dimer phase is caused by the frustration effect. In the dimer phase, there exists an excitation gap between the twofold-degenerate ground state and the first excited state, which explains the non-magnetic ground state observed in Cu3Cl6(H2O)2·2H8C4SO2. We also obtain the phase diagram on the 2 - 3 plane from the numerical diagonalization data for finite systems by use of the Lanczos algorithm.

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Antiferromagnetic model with known ground state

Cited by 250 publications

References 13 publications

Nonergodic dynamics of the extended anisotropic Heisenberg chain

Nonergodic dynamics of the extended anisotropic Heisenberg chain

Entanglement in many-body systems

The ground state of anS= 1/2 distorted diamond chain - a model of Cu₃Cl₆(H₂O)₂·2H₈C₄SO₂

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Antiferromagnetic model with known ground state

Cited by 250 publications

References 13 publications

Nonergodic dynamics of the extended anisotropic Heisenberg chain

Nonergodic dynamics of the extended anisotropic Heisenberg chain

Entanglement in many-body systems

The ground state of anS= 1/2 distorted diamond chain - a model of Cu3Cl6(H2O)2·2H8C4SO2

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The ground state of anS= 1/2 distorted diamond chain - a model of Cu₃Cl₆(H₂O)₂·2H₈C₄SO₂