Density matrix renormalisation group approach to the massive Schwinger model

Byrnes, Tim; Sriganesh, P.; Bursill, Robert J.; Hamer, C. J.

doi:10.1016/s0920-5632(02)01416-0

Cited by 34 publications

(46 citation statements)

References 43 publications

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“…This is the first time that the second vector excitation has been found numerically. For the energy density and the two lowest mass excitations our results are consistent with the previous most precise simulations [2,3], with a similar or sometimes better accuracy. As shown in the supplementary material, we were also able to reconstruct the Einstein dispersion relation for small momenta ka ≪ 1.…”

supporting

confidence: 91%

“…Similar to [2] our extrapolation error is then estimated by considering a third and fourth order polynomial through all six points, taking the error to be the maximal difference with the original inferred value.…”

Section: Special Features Of Gauge Invariant Mpsmentioning

confidence: 99%

“…These fermionic degrees of freedom can then finally be converted to spin 1/2 degrees of freedom by a Jordan-Wigner transformation, leading to the gauged spin Hamiltonian (see [2] for more details):…”

mentioning

confidence: 99%

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Matrix product states for gauge field theories

Acoleyen¹,

Buyens²,

Haegeman³

et al. 2015

Proceedings of the 32nd International Symposium on Lattice Field Theory — PoS(LATTICE2014)

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The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study 1+1 dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground state properties and elementary one-particle excitations in the continuum limit. In particular, a novel particle excitation in the form of a heavy vector boson is uncovered, compatible with the strong coupling expansion in the continuum. We also study full quantum non-equilibrium dynamics by simulating the real-time evolution of the system induced by a quench in the form of a uniform background electric field. PACS numbers:Gauge theories hold a most prominent place in physics. They appear as effective low energy descriptions at different instances in condensed matter physics and nuclear physics. But far and foremost they lie at the root of our understanding of the four fundamental interactions that are each mediated by the gauge fields corresponding to a particular gauge symmetry. At the perturbative quantum level, this picture translates to the Feynman diagrammatic approach that has produced physical predictions with unlevelled precision, most famously in quantum electrodynamics (QED). However the perturbative approach miserably fails once the interactions become strong. This problem is most pressing for quantum chromodynamics (QCD), where all low energy features like quark confinement, chiral symmetry breaking and mass generation are essentially non-perturbative.Lattice QCD, which is based on Monte Carlo sampling of Wilson's Euclidean lattice version of gauge theories, has historically been by far the most successful method in tackling this strongly coupled regime. Using up a sizable fraction of the global supercomputer time, state of the art calculations have now reached impressive accuracy, for instance in the ab initio determination of the light hadron masses [1]. But in spite of its clear superiority, the lattice Monte Carlo sampling also suffers from a few drawbacks. There is the infamous sign problem that prevents application to systems with large fermionic densities. In addition, the use of Euclidean time, as opposed to real time, presents a serious barrier for the understanding of dynamical non-equilibrium phenomena. Over the last few years there has been a growing experimental and theoretical interest in precisely these elusive regimes, e.g. in the study of heavy ion collisions or early time cosmology.In this letter we study the application of tensor network states (TNS) as a possible complementary approach to the numerical simulation of gauge theories. This is highly relevant as this Hamiltonian method is free from the sign problem and allows for real-time dynamics. As a first application we focus on the massive Schwinger model. For this model the TNS approach has been studied before by Byrnes et al [2] and Bañuls et al [3]. By integrating out the ...

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supporting

confidence: 91%

Section: Special Features Of Gauge Invariant Mpsmentioning

confidence: 99%

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Matrix product states for gauge field theories

Acoleyen¹,

Buyens²,

Haegeman³

et al. 2015

Proceedings of the 32nd International Symposium on Lattice Field Theory — PoS(LATTICE2014)

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“…Here we determine the single-particle excitations for different values of α. Surprisingly, earlier numerical studies on the spectrum of the Schwinger model in the non-perturbative regime exclusively focussed on the cases α = 0 [19,23,62] and α = 1/2 [21][22][23]. An overview of the low-energy spectrum is for instance useful to have a better understanding of the dynamics induced by a quench in the form of an electric field.…”

Section: Introductionmentioning

confidence: 99%

Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks

et al. 2017

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It has been established that Matrix Product States can be used to compute the ground state and single-particle excitations and their properties of lattice gauge theories at the continuum limit. However, by construction, in this formalism the Hilbert space of the gauge fields is truncated to a finite number of irreducible representations of the gauge group. We investigate quantitatively the influence of the truncation of the infinite number of representations in the Schwinger model, oneflavour QED2, with a uniform electric background field. We compute the two-site reduced density matrix of the ground state and the weight of each of the representations. We find that this weight decays exponentially with the quadratic Casimir invariant of the representation which justifies the approach of truncating the Hilbert space of the gauge fields. Finally, we compute the single-particle spectrum of the model as a function of the electric background field.

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“…One usually takes the bosonized version of these models which are local selfinteracting scalar theories, and can be investigated in an easier way [11,12]. The phase structure of the QED 2 with many flavors was mapped out from its bosonized version and it was shown that it exhibits only a single phase [13,14] as opposed to the single-flavor QED 2 (which is often referred to as the massive Schwinger model) [3-5, 11, 12], which possesses a symmetric strong coupling (e m e ) phase and the weak coupling (e m e ) phase with spontaneously broken reflection symmetry separated by the critical value (m e /e) c ∼ 0.31 as was shown by density matrix renormalization group (RG) technique [15,16] or by continuous RG method [14,17].…”

Section: Introductionmentioning

confidence: 99%