Spherical Deformation for One-Dimensional Quantum Systems

Gendiar, Andrej; Krčmár, Roman; Nishino, Tomotoshi

doi:10.1143/ptp.122.953

Cited by 66 publications

(85 citation statements)

References 9 publications

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“…20 This result was in fact supported analytically for the noninteracting case. 21 In the results of free fermionic model, 11 the Heisenberg chain [ Fig. 1(c)], and J 1 -J 2 models, which we will see shortly, the translational symmetry is indeed recovered by the deformation.…”

Section: Deformed Interactionsmentioning

confidence: 84%

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Boundary effects in the density-matrix renormalization group calculation

Shibata

Hotta

2011

Phys. Rev. B

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We investigate the boundary effect of the density matrix renormalization group calculation (DMRG), which is an artifactual induction of symmetry-breaking pseudo-long-range order and takes place when the long range quantum fluctuation cannot be properly included in the variational wave function due to numerical limitation. The open boundary condition often used in DMRG suffers from the boundary effect the most severely, which is directly reflected in the distinct spatial modulations of the local physical quantity. By contrast, the other boundary conditions such as the periodic one or the sin 2 -deformed interaction [A. Gendiar, R. Krcmar, and T. Nishino, Prog. Theor. Phys. 122, 953 (2009)] keep spatial homogeneity, and are relatively free from the boundary effect. By comparing the numerical results of those various boundary conditions, we show that the open boundary condition sometimes gives unreliable results even after the finite-size scaling. We conclude that the examination of the boundary condition dependence is required besides the usual treatment based on the system size or accuracy dependence in cases where the long-range quantum fluctuation is important.

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Section: Deformed Interactionsmentioning

confidence: 84%

“…As a typical boundary condition of the former class, we deal with the system with "deformed interactions" recently proposed by Gendiar, Krcmar, and Nishino, 11 as well as the PBC and APBC. The representative condition of the latter class is the OBC.…”

Section: A Symmetry-breaking Long-range Ordersmentioning

confidence: 99%

Boundary effects in the density-matrix renormalization group calculation

Shibata

Hotta

2011

Phys. Rev. B

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“…where L is the length of the system and 0 ≤ x ≤ L. As seen from f x = 0 for x = 1/2 (mod L), the SSD breaks the link between the sites 1 and L. In various 1D systems including free-fermion chains [4], quantum spin chains and ladders [5], the Hubbard model [6], and Kondo-lattice model [7], the performance of the SSD has been examined numerically. It was found for critical systems that the SSD completely suppresses the boundary effects, i.e., the ground-state expectation values of local observables such as the bond strength are translationally invariant.…”

Section: Introductionmentioning

confidence: 99%

Sine-square deformation of solvable spin chains and conformal field theories

Katsura¹

2012

J. Phys. A: Math. Theor.

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Abstract. We study solvable spin chains, one-dimensional massless Dirac fermions, and conformal field theories (CFTs) with sine-square deformation (SSD), in which the Hamiltonian density is modulated by the function f (x) = sin 2 (πx/ℓ), where x is the position and ℓ is the length of the system. For the XY chain and the transverse field Ising chain at criticality, it is shown that the ground state of an open system with SSD is identical to that of a uniform chain with periodic boundary conditions. The same holds for the massless Dirac fermions with SSD, corresponding to the continuum limit of the gapless XY chain. For general CFTs, we find that the Hamiltonian of a system with SSD has an expression in terms of the generators of the Virasoro algebra. This allows us to show that the vacuum state is an exact eigenstate of the sine-square deformed Hamiltonian. Furthermore, for a restricted class of CFTs associated with affine Lie (Kac-Moody) algebras, including c = 1 Gaussian CFT, we prove that the vacuum is an exact ground state of the deformed Hamiltonian. This explains why the SSD has succeeded in suppressing boundary effects in one-dimensional critical systems, as observed in previous numerical studies.

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“…To overcome this difficulty, here we use the ground canonical analysis with the sine-square deformation (SSD) that has been developed recently [25][26][27][28]. The SSD deforms the original Hamiltonian of Eq.…”

mentioning

confidence: 99%

Multiple magnetization plateaus and magnetic structures in theS=12Heisenberg model on the checkerboard lattice

Morita

Shibata

2016

Phys. Rev. B

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We study the ground state of S = 1/2 Heisenberg model on the checkerboard lattice in a magnetic field by the density matrix renormalization group (DMRG) method with the sine-square deformation. We obtain magnetization plateaus at M/Msat =0, 1/4, 3/8, 1/2, and 3/4 where Msat is the saturated magnetization. The obtained 3/4 plateau state is consistent with the exact result, and the 1/2 plateau is found to have a four-spin resonating loop structure similar to the six-spin loop structure of the 1/3 plateau of the kagome lattice. Different four-spin loop structures are obtained in the 1/4 and 3/8 plateaus but no corresponding states exist in the kagome lattice. The 3/8 plateau has a unique magnetic structure of three types of four-spin local quantum states in a 4 √ 2 × 2 √ 2 magnetic unit cell with a 16-fold degeneracy.Frustrated quantum spin systems exhibit unusual quantum phenomena such as the formations of valence bond solid (VBS), spin-nematic, and quantum spin liquid (QSL) as a result of competing quantum fluctuations [1,2]. Application of an external magnetic field complicates the situation further with the increase in uniaxial anisotropy, and it sometimes leads to a phase transition to a stable quantum state with a jump or cusp in the magnetization curve at zero temperature. Recently observed 1/3 magnetization plateau in the triangular lattice of S = 1/2 quantum spins [3-5] is a typical example, in which up-up-down spin structure emerges with a finite excitation gap [6][7][8][9]. Similar 1/2 plateau is obtained in the J 1 -J 2 square lattice [9-11] and novel multiple magnetization plateaus are realized in the Shastry-Sutherland lattice [12][13][14][15]. In the kagome lattice, 0, 1/9, 1/3, 5/9, and 7/9 plateaus are predicted by the DMRG method with the sine-square deformation [16].The checkerboard lattice shown in Fig. 1 is another example of frustrated system and referred to as twodimensional pyrochlore lattice. Its classical ground state at zero magnetic field is obtained when the magnetic moments of four spins connected by diagonal interactions are canceled as shown in Fig. 2. This means the presence of a macroscopic degeneracy in the ground state as in the cases of the kagome lattice and the J 1 -J 2 square lattice at J 2 /J 1 = 0.5. In contrast, S = 1/2 quantum spins on the checkerboard lattice have stable quantum ground state as in the kagome lattice [16][17][18] and Shastry-Sutherland lattice [12][13][14][15]. Indeed previous studies on the checkerboard lattice indicate that the ground state is a plaquette valence-bond crystal (PVBC) with a large spin singlettriplet gap, ∆ st ≈ 0.6J [19,20] and the 3/4 plateau is realized just before the saturation magnetic field [21] as in the case of the 7/9 plateau in the kagome lattice [22].Although the ideal checkerboard lattice with only one exchange energy J has not been synthesized, similar model substances are present [23,24]. The checkerboard lattice is obtained by replacing the position of anions and cations in the CuO 2 -plane structure. When the nearest-neig...

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Spherical Deformation for One-Dimensional Quantum Systems

Cited by 66 publications

References 9 publications

Boundary effects in the density-matrix renormalization group calculation

Boundary effects in the density-matrix renormalization group calculation

Sine-square deformation of solvable spin chains and conformal field theories

Multiple magnetization plateaus and magnetic structures in theS=12Heisenberg model on the checkerboard lattice

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