Doubling of entanglement spectrum in tensor renormalization group

Ueda, Hiroshi; Okunishi, Kouichi; Nishino, Tomotoshi

doi:10.1103/physrevb.89.075116

Cited by 37 publications

(57 citation statements)

References 49 publications

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“…The decay is rapid, and therefore further increase of the number of block-spin state from D = 24 to a larger number does not significantly improve the precision in Z n ; the difference in f (T c ) between D = 8 and D = 16 is already of the order of 10 −6 . It should be noted that the eigenvalues are not distributed equidistantly in logarithmic scale; the corner double line structure is absent 24,25 .…”

Section: Numerical Resultsmentioning

confidence: 99%

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Phase transition of the Ising model on a fractal lattice

2016

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Phase transition of the Ising model is investigated on a planar lattice that has a fractal structure. On the lattice, the number of bonds that cross the border of a finite area is doubled when the linear size of the area is extended by a factor of four. The free energy and the spontaneous magnetization of the system are obtained by means of the higher-order tensor renormalization group method. The system exhibits the order-disorder phase transition, where the critical indices are different from that of the square-lattice Ising model. An exponential decay is observed in the density matrix spectrum even at the critical point. It is possible to interpret that the system is less entangled because of the fractal geometry.

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Section: Numerical Resultsmentioning

confidence: 99%

“…The fractal structure of the lattice modifies the entanglement spectrum from that on the square lattice explained by the corner double line picture 24,25 . Since each corner is missing in the fractal structure in Fig.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Phase transition of the Ising model on a fractal lattice

2016

Self Cite

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“…[82,83] that the correlation length ξ determined by the MPS wave function at the critical point serves as this finite length scale. The finite correlation length stems from the finite entanglement properties for finite D MPS, so this approach is also known as finite entanglement scaling [84][85][86][87]. For a normalized MPS wave function with a given D, the effective correlation length ξ can be easily evaluated as…”

Section: Matrix Product State and Finite Correlation Length Scalingmentioning

confidence: 99%

Emergent symmetry and conserved current at a one-dimensional incarnation of deconfined quantum critical point

Huang

You

et al. 2019

Phys. Rev. B

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The deconfined quantum critical point (DQCP) was originally proposed as a continuous transition between two spontaneous symmetry breaking phases in 2D spin-1/2 systems. While great efforts have been spent on the DQCP for 2D systems, both theoretically and numerically, ambiguities among the nature of the transition are still not completely clarified. Here we shift the focus to a recently proposed 1D incarnation of DQCP in a spin-1/2 chain. By solving it with the variational matrix product state in the thermodynamic limit, a continuous transition between a valence-bond solid phase and a ferromagnetic phase is discovered. The scaling dimensions of various operators are calculated and compared with those from field theoretical description. At the critical point, two emergent O(2) symmetries are revealed, and the associated conserved current operators with exact integer scaling dimensions are determined with scrutiny. Our findings provide the low-dimensional analog of DQCP where unbiased numerical results are in perfect agreement with the controlled field theoretical predictions and have extended the realm of the unconventional phase transition as well as its identification with the advanced numerical methodology.

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“…Several previous papers concentrated on the Ising model [7,11] or phase boundaries of spin 1 models [5]. The XXZ model has a rich phase structure including a extended critical phase.…”

Section: Discussionmentioning

confidence: 99%

“…This enables significantly more detailed investigations and tests than those previously available. Most studies up to now concentrated either on the classical or quantum Ising model [4,7,10,11] or the phase boundaries only [5]. The low-lying spectrum is not usually considered, since precision calculations require large tensor sizes.…”

Section: Introductionmentioning

confidence: 99%

Spin- 12 XXZ Heisenberg chain in a longitudinal magnetic field

Rakov

Weyrauch

2019

Phys. Rev. B

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We study the XXZ Heisenberg model in a longitudinal magnetic field using a tensor renormalization method. Built into the tensor representation of the XXZ model is the U(1) symmetry, which is systematically maintained at each renormalization step. This enables rather large tensor representations. We extract ground state properties as well as the low lying spectrum from the fixed point tensors. With rather moderate numerical effort we achieve a very good accuracy as demonstrated by comparison with Bethe Ansatz calculations. The phase structure of the model can be accurately reproduced just from the largest fixed point tensor elements.

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Doubling of entanglement spectrum in tensor renormalization group

Cited by 37 publications

References 49 publications

Phase transition of the Ising model on a fractal lattice

Phase transition of the Ising model on a fractal lattice

Emergent symmetry and conserved current at a one-dimensional incarnation of deconfined quantum critical point

Spin- 12 XXZ Heisenberg chain in a longitudinal magnetic field

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