Coarse-graining renormalization by higher-order singular value decomposition

Xie, Z. Y.; Chen, Jing; Qin, Mingpu; Zhu, Jianming; Yang, Liping; Xiang, Tao

doi:10.1103/physrevb.86.045139

Cited by 407 publications

(632 citation statements)

References 49 publications

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“…A TRG method based on the higherorder SVD, which was proposed in Ref. [25], is the most effective approach to higher dimensional systems at the moment. Its computational cost, however, is proportional to D 15 for a 4D hypercubic lattice, which is still too expensive.…”

Section: Discussionmentioning

confidence: 99%

Grassmann tensor renormalization group approach to one-flavor lattice Schwinger model

2014

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We apply the Grassmann tensor renormalization group to the lattice regularized Schwinger model with one-flavor of the Wilson fermion. We study the phase diagram in the ðβ; κÞ plane performing a detailed analysis of the scaling behavior of the Lee-Yang zeros and the peak height of the chiral susceptibility. Our results strongly indicate that the whole range of the phase transition line starting from ðβ; κÞ ¼ ð0.0; 0.380665ð59ÞÞ and ending at ð∞; 0.25Þ belongs to the two-dimensional Ising universality class similar to the free fermion case.

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Section: Discussionmentioning

confidence: 99%

Grassmann tensor renormalization group approach to one-flavor lattice Schwinger model

2014

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“…Their original manifestation, the density-matrix renormalization group (DMRG) [7], is now understood to be based on a variational update of a matrix product state (vMPS) [8,9], and has found applications in a wide range of fields such as quantum chemistry [10] and quantum information [11] as well as condensed matter physics [12]. More recent developments have extended the methods to, e.g., critical systems [13], two-dimensional lattices [14][15][16], and topologically ordered states [17].…”

Section: Introductionmentioning

confidence: 99%

Self-assembling tensor networks and holography in disordered spin chains

Goldsborough

Römer

2014

Phys. Rev. B

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We show that the numerical strong disorder renormalization group algorithm of Hikihara et al. [Phys. Rev. B 60, 12116 (1999)] for the one-dimensional disordered Heisenberg model naturally describes a tree tensor network (TTN) with an irregular structure defined by the strength of the couplings. Employing the holographic interpretation of the TTN in Hilbert space, we compute expectation values, correlation functions, and the entanglement entropy using the geometrical properties of the TTN. We find that the disorder-averaged spin-spin correlation scales with the average path length through the tensor network while the entanglement entropy scales with the minimal surface connecting two regions. Furthermore, the entanglement entropy increases with both disorder and system size, resulting in an area-law violation. Our results demonstrate the usefulness of a self-assembling TTN approach to disordered systems and quantitatively validate the connection between holography and quantum many-body systems.

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“…In the past years, the tensor network algorithms have been widely developed [3][4][5][6][7][8][9][10][11][12][13][14][15] , which are shown to be promising numerical tools. One of the simplest tensor network state is the matrix product state (MPS), which is the variational wave function of the DMRG method 16,17 .…”

Section: Introductionmentioning

confidence: 99%

Variational Monte Carlo method for fermionic models combined with tensor networks and applications to the hole-doped two-dimensional Hubbard model

et al. 2017

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The conventional tensor-network states employ real-space product states as reference wave functions. Here, we propose a many-variable variational Monte Carlo (mVMC) method combined with tensor networks by taking advantages of both to study fermionic models. The variational wave function is composed of a pair product wave function operated by real space correlation factors and tensor networks. Moreover, we can apply quantum number projections, such as spin, momentum and lattice symmetry projections, to recover the symmetry of the wave function to further improve the accuracy. We benchmark our method for one-and two-dimensional Hubbard models, which show significant improvement over the results obtained individually either by mVMC or by tensor network. We have applied the present method to hole doped Hubbard model on the square lattice, which indicates the stripe charge/spin order coexisting with a weak d-wave superconducting order in the ground state for the doping concentration less than 0.3, where the stripe oscillation period gets longer with increasing hole concentration. The charge homogeneous and highly superconducting state also exists as a metastable excited state for the doping concentration less than 0.25.

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Coarse-graining renormalization by higher-order singular value decomposition

Cited by 407 publications

References 49 publications

Grassmann tensor renormalization group approach to one-flavor lattice Schwinger model

Grassmann tensor renormalization group approach to one-flavor lattice Schwinger model

Self-assembling tensor networks and holography in disordered spin chains

Variational Monte Carlo method for fermionic models combined with tensor networks and applications to the hole-doped two-dimensional Hubbard model

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