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

Katsura, Hosho

doi:10.1088/1751-8113/45/11/115003

Cited by 73 publications

(94 citation statements)

References 59 publications

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“…Another interesting class of deformations are Möbius deformations and the sine-square deformation (SSD). [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] Starting from the uniform system defined on a spatial circle of circumference L, the Möbius evolution is given by…”

Section: B Möbius and Ssd Deformationsmentioning

confidence: 99%

Holographic duals of inhomogeneous systems: the rainbow chain and the sine-square deformation model

MacCormack¹,

Liu²,

Ryu³

2019

J. Phys. A: Math. Theor.

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A holographic dual description of inhomogeneous systems is discussed. Notably, finite temperature results for the entanglement entropy in both the rainbow chain and the SSD model are obtained holographically by choosing appropriate foliations of the BTZ spacetime. Other inhomogeneous theories are also discussed. The entanglement entropy results are verified numerically, indicating that a wide variety of inhomogeneous field theory phenomenology can be seen in different slicings of asymptotically AdS3 spacetimes.CONTENTS arXiv:1812.10023v1 [cond-mat.str-el]

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Section: B Möbius and Ssd Deformationsmentioning

confidence: 99%

Holographic duals of inhomogeneous systems: the rainbow chain and the sine-square deformation model

MacCormack¹,

Liu²,

Ryu³

2019

J. Phys. A: Math. Theor.

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“…It serves as one of the boundary conditions [22][23][24][25], as well as works as a real-space renormalization scheme [26]. It also reveals itself as one of a low energy effective Hamiltonian in a 2D conformal field theory [27][28][29]. Moreover, adiabatic connections between the uniform and SSD Hamiltonian is guaranteed [30].…”

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confidence: 99%

Magnetic susceptibility of quantum spin systems calculated by sine square deformation: One-dimensional, square lattice, and kagome lattice Heisenberg antiferromagnets

Hotta

Asano

2018

Phys. Rev. B

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We develop a simple and unbiased numerical method to obtain the uniform susceptibility of quantum many body systems. When a Hamiltonian is spatially deformed by multiplying it with a sine square function that smoothly decreases from the system center toward the edges, the sizescaling law of the excitation energy is drastically transformed to a rapidly converging one. Then, the local magnetization at the system center becomes nearly size independent; the one obtained for the deformed Hamiltonian of a system length as small as L ∼ 10 provides the value obtained for the original uniform Hamiltonian of L ∼ 100. This allows us to evaluate a bulk magnetic susceptibility by using the magnetization at the center by existing numerical solvers without any approximation, parameter tuning, or the size-scaling analysis. We demonstrate that the susceptibilities of the spin-1/2 antiferromagnetic Heisenberg chain and square lattice obtained by our scheme at L ∼ 10 agree within 10 −3 with exact analytical and numerical solutions for L = ∞ down to temperature of 0.1 times the coupling constant. We apply this method to the spin-1/2 kagome lattice Heisenberg antiferromagnet which is of prime interest in the search of spin liquids.

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“…We closely follow Ref. [22] to show that the ground state |ψ G of H QIM (g) with even (odd) number of sites has an even (odd) fermion parity for g > 0. Using the basis in which σ x j is diagonalized, i.e., | → j = (| ↑ j + | ↓ j )/ √ 2, | ← j = (| ↑ j − | ↓ j )/ √ 2, all of the offdiagonal elements of H QIM are nonpositive and satisfy the connectivity condition (note that σ z j | → / ← j = | ← / → j ).…”

Section: Discussionmentioning

confidence: 82%

Longitudinal magnetization dynamics in the quantum Ising ring: A Pfaffian method based on correspondence between momentum space and real space

2020

Phys. Rev. E

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As perhaps the most studied paradigm for a quantum phase transition, the periodic quantum Ising chain is exactly solvable via the Jordan-Wigner transformation followed by a Fourier transform that diagonalizes the model in the momentum space of spinless fermions. Although the above procedures are well-known, there remain some subtle points to be clarified regarding the correspondence between the real-space and momentum-space representations of the finite-size quantum Ising ring, especially those related to fermion parities. In this work, we establish the relationship between the two fully aligned ferromagnetic states in real space and the two degenerate momentum-space ground states of the classical Ising ring, with the former being a special case of the factorized ground states of the more general XYZ model on the frustration-free hypersurface. Based on this observation, we then provide a Pfaffian formula for calculating real-time dynamics of the parity-breaking longitudinal magnetization with the system initially prepared in one of the two ferromagnetic states and under translationally invariant drivings. The formalism is shown to be applicable to large systems with the help of online programs for the numerical computation of the Pfaffian, thus providing an efficient method to numerically study, for example, the emergence of discrete time crystals in related systems.

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

Cited by 73 publications

References 59 publications

Holographic duals of inhomogeneous systems: the rainbow chain and the sine-square deformation model

Holographic duals of inhomogeneous systems: the rainbow chain and the sine-square deformation model

Magnetic susceptibility of quantum spin systems calculated by sine square deformation: One-dimensional, square lattice, and kagome lattice Heisenberg antiferromagnets

Longitudinal magnetization dynamics in the quantum Ising ring: A Pfaffian method based on correspondence between momentum space and real space

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