Efficient MPS Algorithm for Periodic Boundary Conditions and Applications Section: Solid matter Original Author's Text: English Abstract: We present the implementation of an efficient algorithm for the calculation of the spectrum of one-dimensional quantum systems with periodic boundary conditions. This algorithm is based on a matrix product representation for quantum states (MPS) and a similar representation for Hamiltonians and other operators (MPO). It is significantly more efficient for systems of abou

Weyrauch, M.; Rakov, Mykhailo V.

doi:10.15407/ujpe58.07.0657

Cited by 8 publications

(3 citation statements)

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“…An MPS formalism for PBC was originally proposed in [52] and extended in [21,53]. We summarized the algorithm in [54,55], and therefore we only briefly review here those aspects which are relevant for the present discussion.…”

Section: Review: the Mps Formalism For Pbcmentioning

confidence: 99%

Bilinear-biquadratic spin-1 rings: an SU(2)-symmetric MPS algorithm for periodic boundary conditions

Rakov¹,

Weyrauch²

2017

J. Phys. Commun.

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An efficient algorithm for SU(2) symmetric matrix product states with periodic boundary conditions is proposed and implemented. It is applied to a study of the spectrum and correlation properties of the spin-1 bilinear-biquadratic Heisenberg model. We characterize the various phases of this model by the lowest states of the spectrum with angular momentum J 0, 1, 2 = for systems of up to 100 spins. Furthermore, we provide precision results for the dimerization correlator as well as the string correlator.

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Section: Review: the Mps Formalism For Pbcmentioning

confidence: 99%

Bilinear-biquadratic spin-1 rings: an SU(2)-symmetric MPS algorithm for periodic boundary conditions

Rakov¹,

Weyrauch²

2017

J. Phys. Commun.

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“…Due to this reason, the usual approach of DMRG-MPS does not work efficiently for PBC, because the dimension of the local matrices is quite big due to long-range spin interactions. In this context, there is another approach based on the transfer-matrix [7][8][9] which has tackled the problem of dealing with PBC with encouraging results. In this paper, we will particularly talk about Hamiltonians of one-dimensional spin chain models with PBC and we will give a generalized universal approach of decomposing a Hamiltonian into MPOs, later these will be used in the DMRG algorithm to validate our results.…”

Section: Introductionmentioning

confidence: 99%

A new general approach for obtaining matrix product operators for spin Hamiltonians with periodic boundary conditions

Solanki¹,

Ramkarthik²

2023

Phys. Scr.

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This article concerns the matrix product operators for one-dimensional spin Hamiltonians under open and periodic boundary conditions. A novel approach called `the dynamics of blocks' is proposed to obtain the matrix product operators in the case of Hamiltonians with periodic boundary conditions. This approach works universally for any Hamiltonian with two-particle as well as single-particle interactions. The main significance of the proposed approach is that, the dimensions of the matrix product operators obtained are the same for both open and periodic boundary conditions. This method gives us a generic way of constructing MPOs for any Hamiltonian with arbitrary neighboring interactions, immaterial of how the interaction strength falls. A general numerical implementation of the `dynamics of blocks' method is also carried out. The DMRG algorithm was implemented, and the ground state eigenvalue was obtained using these MPOs to numerically validate the method.

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“…It is the purpose of the present paper to address this discrepancy using variants of both methods in parallel. To this end we determine both the spectrum as well as the order parameter at θ = − π 2 as a function of the Zeeman coupling D. Calculations will be performed for systems with periodic boundary conditions (spin rings) using our own matrix product state (MPS) algorithm for systems up to 100 sites [6][7][8].…”

Section: Introductionmentioning

confidence: 99%