Time evolution of an infinite projected entangled pair state: An efficient algorithm

Czarnik, Piotr; Dziarmaga, Jacek; Corboz, Philippe

doi:10.1103/physrevb.99.035115

Cited by 110 publications

(148 citation statements)

References 80 publications

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“…Further details concerning the iPEPS ansatz and algorithms for thermal states may be found in Ref. [36].…”

Section: A T E X I T S H a 1 _ B A S E 6 4 = " C N S Z X B 6 B 9 Z mentioning

confidence: 99%

“…In fact this ansatz provides not only a compact representation for the ground states of gapped local Hamiltonians, but also for representing a purification of the thermal density operator, and hence the thermal states of local Hamiltonians. Here we exploit newly developed algorithms [36] allowing the efficient calculation of imaginary-time evolution processes, which in general require additional truncation to retain the value of D at each time step, to generate thermal states of the Shastry-Sutherland Hamiltonian and hence to compute its thermodynamic properties.…”

Section: Introductionmentioning

confidence: 99%

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Thermodynamic properties of the Shastry-Sutherland model throughout the dimer-product phase

Wietek

Corboz

Weßel

et al. 2019

Phys. Rev. Research

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The thermodynamic properties of the Shastry-Sutherland model have posed one of the longestlasting conundrums in frustrated quantum magnetism. Over a wide range on both sides of the quantum phase transition (QPT) from the dimer-product to the plaquette-based ground state, neither analytical nor any available numerical methods have come close to reproducing the physics of the excited states and thermal response. We solve this problem in the dimer-product phase by introducing two qualitative advances in computational physics. One is the use of thermal pure quantum (TPQ) states to augment dramatically the size of clusters amenable to exact diagonalization. The second is the use of tensor-network methods, in the form of infinite projected entangled pair states (iPEPS), for the calculation of finite-temperature quantities. We demonstrate convergence as a function of system size in TPQ calculations and of bond dimension in our iPEPS results, with complete mutual agreement even extremely close to the QPT. Our methods reveal a remarkably sharp and low-lying feature in the magnetic specific heat around the QPT, whose origin appears to lie in a proliferation of excitations composed of two-triplon bound states. The surprisingly low energy scale and apparently extended spatial nature of these states explain the failure of less refined numerical approaches to capture their physics. Both of our methods will have broad and immediate application in addressing the thermodynamic response of a wide range of highly frustrated magnetic models and materials.

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“…Further details concerning the iPEPS ansatz and algorithms for thermal states may be found in Ref. [36].…”

Section: A T E X I T S H a 1 _ B A S E 6 4 = " C N S Z X B 6 B 9 Z mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermodynamic properties of the Shastry-Sutherland model throughout the dimer-product phase

Wietek

Corboz

Weßel

et al. 2019

Phys. Rev. Research

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“…While the finite color order of the dimer phase can only exist at zero temperature in two dimensions, the dimerization may in principle set in already at finite temperature (without coexisting color order), or occur simultaneously with the color order at zero temperature. Recently developed tensor network approaches for finitetemperature simulations [88][89][90][91][92][93] may provide further insights into the critical temperatures in the future.…”

Section: Discussionmentioning

confidence: 99%

SU(3) fermions on the honeycomb lattice at 13 filling

Chung

Corboz

2019

Phys. Rev. B

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SU(N ) symmetric fermions on a lattice, which can be realized in ultracold-atom-based quantum simulators, have very promising prospects for realizing exotic states of matter. Here we present the ground state phase diagram of the repulsive SU(3) Hubbard model on a honeycomb lattice at 1/3 filling obtained from infinite projected entangled pair states tensor network calculations. In the strongly interacting limit the ground state has plaquette order. Upon decreasing the interaction strength U/t we find a first order transition at U/t = 7.2(2) into a dimerized, color-ordered state, which extends down to U/t = 4.5(5) at which the Mott transition occurs and the ground state becomes uniform. Our results may serve as a prediction and benchmark for future quantum simulators of SU(3) fermions.

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“…A TN operator is regarded as a mapping from the bra to the ket Hilbert space. Many algorithms explicitly employ the TN operator form, including the matrix product operator (MPO) for representing 1D many-body operators and mixed states, and for simulating 1D systems in and out of equilibrium [186,187,188,189,190,191,192,193,194,195,196], tensor product operator (also called projected entangled pair operators) in for higher-systems [140,141,143,197,198,199,200,201,202,203,204,205,206], and multiscale entangled renormalization ansatz [207,208,209].…”

Section: Tensor Network States In Two Dimensionsmentioning

confidence: 99%

Tensor Network Contractions

Ran

Tirrito

Peng

et al. 2020

Lecture Notes in Physics

105

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PrefaceTensor network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum information science, statistical physics, and so on. In this lecture notes, we focus on the contraction algorithms of TN as well as some of the applications to the simulations of quantum many-body systems. Starting from basic concepts and definitions, we first explain the relations between TN and physical problems, including the TN representations of classical partition functions, quantum many-body states (by matrix product state, tree TN, and projected entangled pair state), time evolution simulations, etc. These problems, which are challenging to solve, can be transformed to TN contraction problems. We present then several paradigm algorithms based on the ideas of the numerical renormalization group and/or boundary states, including density matrix renormalization group, time-evolving block decimation, coarsegraining/corner tensor renormalization group, and several distinguished variational algorithms. Finally, we revisit the TN approaches from the perspective of multilinear algebra (also known as tensor algebra or tensor decompositions) and quantum simulation. Despite the apparent differences in the ideas and strategies of different TN algorithms, we aim at revealing the underlying relations and resemblances in order to present a systematic picture to understand the TN contraction approaches. v AcknowledgementsWe are indebted to

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Time evolution of an infinite projected entangled pair state: An efficient algorithm

Cited by 110 publications

References 80 publications

Thermodynamic properties of the Shastry-Sutherland model throughout the dimer-product phase

Thermodynamic properties of the Shastry-Sutherland model throughout the dimer-product phase

SU(3) fermions on the honeycomb lattice at 13 filling

Tensor Network Contractions

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