Luttinger liquid physics from the infinite-system density matrix renormalization group

Karrasch, Christoph; Moore, Joel E.

doi:10.1103/physrevb.86.155156

Cited by 31 publications

(43 citation statements)

References 49 publications

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“…This energy scale vanishes at the phase transition. 29 Thus, if the range of accessible energies is bounded from below, e.g. by finite size effects, it might be impossible to observe the physics of the field theory.…”

Section: B Renormalization Group Arguments and Scalingmentioning

confidence: 99%

Universal quench dynamics of interacting quantum impurity systems

2014

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The equilibrium physics of quantum impurities frequently involves a universal crossover from weak to strong reservoir-impurity coupling, characterized by single-parameter scaling and an energy scale TK (Kondo temperature) that breaks scale invariance. For the non-interacting resonant level model, the non-equilibrium time evolution of the Loschmidt echo after a local quantum quench was recently computed explicitly [R. Vasseur, K. Trinh, S. Haas, and H. Saleur, Phys. Rev. Lett. 110, 240601 (2013)]. It shows single-parameter scaling with variable TK t. Here, we scrutinize whether similar universal dynamics can be observed in various interacting quantum impurity systems. Using density matrix and functional renormalization group approaches, we analyze the time evolution resulting from abruptly coupling two non-interacting Fermi or interacting Luttinger liquid leads via a quantum dot or a direct link. We also consider the case of a single Luttinger liquid lead suddenly coupled to a quantum dot. We investigate whether the field theory predictions for the universal scaling as well as for the large time behavior successfully describe the time evolution of the Loschmidt echo and the entanglement entropy of microscopic models. Our study shows that for the considered local quench protocols the above quantum impurity models fall into a class of problems for which the non-equilibrium dynamics can largely be understood based on the knowledge of the corresponding equilibrium physics.

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Section: B Renormalization Group Arguments and Scalingmentioning

confidence: 99%

Universal quench dynamics of interacting quantum impurity systems

2014

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“…There has been additional validation on the experimental front, at least qualitatively; several realizations, ranging from carbon nanotubes [20,21] to semiconductor wires [22], of TLL physics have been found. Quantitative estimates of the scaling dimensions, velocity, and Luttinger parameter for model Hamiltonians have been made with analytic solutions or numerically, with exact diagonalization and density matrix renormalization group [23] methods [15,[24][25][26][27]]. Most theoretical studies have focused on the single component TLL, which directly corresponds to a c = 1 CFT, and which now appears to be a fairly well understood case [15,18].…”

Section: Introductionmentioning

confidence: 99%

Determination of Tomonaga-Luttinger parameters for a two-component liquid

et al. 2015

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We provide evidence for the mapping of critical spin-1 chains, in particular the SU(3) symmetric bilinearbiquadratic model with additional interactions, to free boson theories using exact diagonalization and the density matrix renormalization group algorithm. Using the correspondence with a conformal field theory with central charge c = 2, we determine the analytic formulae for the scaling dimensions in terms of four TomonagaLuttinger liquid parameters. By matching the lowest scaling dimensions, we numerically calculate these fieldtheoretic parameters and track their evolution as a function of the parameters of the lattice model.

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“…Thermodynamic quantities given by the Bethe ansatz can be combined with LL-theory to obtain various correlation functions [29]. Additionally, the numerical density-matrix-renormalization-group (DMRG) gives accurate predictions in this limit [30,31] used to benchmark the LL [32]. The situation gets more involved for the full model(5), since Bethe-ansatz integrability is lost, and DMRG with long-range interactions is more intricate (i.e.…”

Section: Bosonization and Mpsmentioning

confidence: 99%

“…The situation gets more involved for the full model(5), since Bethe-ansatz integrability is lost, and DMRG with long-range interactions is more intricate (i.e. typically, models with only a few neighbours are studied [32]).…”

Section: Bosonization and Mpsmentioning

confidence: 99%

Driven spin-boson Luttinger liquids

2015

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We introduce a lattice model of interacting spins and bosons that leads to Luttinger-liquid physics, and allows for quantitative tests of the theory of bosonization by means of trapped-ion or superconducting-circuit experiments. By using a variational bosonization ansatz, we calculate the power-law decay of spin and boson correlation functions, and study their dependence on a single tunable parameter, namely a bosonic driving. For small drivings, matrix-product-states (MPSs) numerical methods are shown to be efficient and validate our ansatz. Conversely, even static MPS become inefficient for large-driving regimes, such that the experiment can potentially outperform classical numerics, achieving one of the goals of quantum simulations.

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Luttinger liquid physics from the infinite-system density matrix renormalization group

Cited by 31 publications

References 49 publications

Universal quench dynamics of interacting quantum impurity systems

Universal quench dynamics of interacting quantum impurity systems

Determination of Tomonaga-Luttinger parameters for a two-component liquid

Driven spin-boson Luttinger liquids

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