Phase diagram of the frustrated spin ladder

Hikihara, Takashi; Starykh, Oleg A.

doi:10.1103/physrevb.81.064432

Cited by 62 publications

(98 citation statements)

References 49 publications

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“…These values are known to be deep in the CD phase for ferromagnetic couplings. 22,23,25 In Fig. 3(b), we plot the fidelity per lattice site d for the number of initial trial states n. In the CD phase it is clearly observed in the same way that there exist two degenerate ground-states corresponding to the two values of d. In fact, for a large enough number of random initial state trials, the probability P(n) of each degenerate ground-state approaches 1/2, i.e., lim n→∞ P(n) = 1/2.…”

Section: Detecting Non-degenerate Ground-statementioning

confidence: 99%

“…18,20 On the other hand, further numerical work provided evidence supporting the existence of the CD phase. 21,22 In particular, the CD phase was claimed to exist in the range 0.373 ≤ J ⊥ ≤ 0.386 for J × = 0.2. 22 This point was further addressed by more extensive density-matrix renormalization group (DMRG) calculations in the range 0.36 ≤ J ⊥ ≤ 0.4 for J × = 0.2, from which it was concluded that the CD phase does not appear.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Detecting Non-degenerate Ground-statementioning

confidence: 99%

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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“…A large λ ǫ < 0 indicates a staggered dimer order on the 2D lattice while λ ǫ > 0 gives a herringbone dimer structure. Depending on the microscopic couplings, it is also possible for the system to acquire a dimerized or magnetically ordered ground state when one of the marginal couplings λ a or λ b , respectively, reaches first the strong coupling limit [63,64]. Finally, the relevant coupling constant λ c with scaling dimension d c = 3/2 may also become largest, a case where no simple order can be assigned to the 2D system and a spin liquid phase is possible.…”

mentioning

confidence: 99%

“…We now proceed to numerically integrate the RG equations (6) for different lattice parameters until one of the couplings becomes unity [55,64]. The constant Ω in the definition of the initial values in Eq.…”

mentioning

confidence: 99%

Spin-liquid versus dimer phases in an anisotropicJ1-J2frustrated square antiferromagnet

2014

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The spin-1/2 J1-J2 antiferromagnet is a prototypical model for frustrated magnetism and one possible candidate for a realization of a spin liquid phase. The generalization of this system on the anisotropic square lattice is given by the J1-J2-J In the search of exotic quantum states and quantum phase transitions, frustrated antiferromagnetic systems have increasingly become the center of attention [1,2]. The competing interactions between spins potentially lead to a large entropy even at low temperatures, which together with quantum fluctuations may give rise to quantum phases with unconventional or topological order parameters [3][4][5]. In particular, the so-called spin liquid state without long range order of a conventional (local) order parameter has been much discussed in the literature ever since Anderson related this phase to hightemperature superconductivity [6]. A solid proof for a system which shows a spin liquid ground state has long been elusive, due to inherent numerical and analytical problems in frustrated systems. Nonetheless, some good evidence for possible spin liquid states has recently been presented for the Hubbard model on the honeycomb [7] and the anisotropic triangular lattice [8], as well as for for the Heisenberg model on a Kagome lattice [1, 9-11], and on the J 1 -J 2 frustrated square lattice [12][13][14].In particular, the J 1 -J 2 Heisenberg model has been treated with a vast array of theoretical methods , which is also the model originally considered by Anderson [6]. Early numerical works have shown an intermediate phase between ordinary Néel order for J 2 0.4J 1 and collinear Néel order for J 2 0.6J 1 [15], but the underlying correlations in this phase remain hotly debated. Most works have predicted a plaquette or columnar dimer order as the most likely scenario [16][17][18][19][20][21][22][23][24][25][26], but more recent numerical works have again proposed a spin liquid [12][13][14]. Unfortunately, the issue may never be conclusively solved using numerical methods, since convergence with finite size and/or temperature of data from density matrix renormalization group (DMRG) or tensor matrix methods is very slow. In particular, it was shown recently for the related two-dimensional (2D) J-Q model that the finite size scaling on moderate lengths would lead to the prediction of a spin liquid, even though the system orders in the thermodynamic limit [44]. In general, the slow convergence is related to the observation that spin liquid states are often very close in energy to competing states with dimer order [10,11].In light of the disappointing numerical situation, analytical methods become very important, but the problem is difficult since series expansions [16,36], chain meanfield theories [45], spin wave theories [23] or coupled cluster methods [25,40,41] have to incorporate frustrating

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“…Frustration can also arise due to competing interactions such coupling (to be discussed later in this chapter), and in spin ladder compounds [39] where frustrated interchain exchange interactions occur both on rungs and diagonals. Since frustration results in multi-degenerate ground states rather than one unique stable one, introduction of very small perturbations or fluctuations in the system cause very novel and exotic phenomena to emerge many of which have not been well explained or understood yet.…”

Section: Frustrationmentioning

confidence: 99%

Low-temperature nuclear magnetic resonance investigation of systems frustrated by competing exchange interactions

Roy¹

2014

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Phase diagram of the frustrated spin ladder

Cited by 62 publications

References 49 publications

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

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

Spin-liquid versus dimer phases in an anisotropicJ1-J2frustrated square antiferromagnet

Low-temperature nuclear magnetic resonance investigation of systems frustrated by competing exchange interactions

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