Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

Nocera, Alberto; Álvarez, Gonzalo

doi:10.1103/physreve.94.053308

Cited by 85 publications

(80 citation statements)

References 47 publications

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“…where we subtract the ground-state expectation value in order to calculate only the dynamical spin fluctuations. These dynamical correlators are calculated using DMRG within the correction-vector formulation in Krylov space [48,49]. In general, these functions are Fourier transformed into the crystal momentum domain to calculate the momentum-energy resolved spectra that is relevant to experiments:…”

Section: Operators and Observablesmentioning

confidence: 99%

“…In the Kitaev model (at zero field) indeed most of the weight in S tot (k, ω) is concentrated at small ω [4]. We test this assumption in the new QSL phase by calculating the numerically challenging dynamical spin structure factor [48,49] at low energies S tot (k, ω = 0) on 8 × 3 unit cell (48 sites) cluster. We find that the dynamical spin structure factor also shows peaks at the M points for ω = 0 (see supplemental), justifying our method to reconstruct the spinon Fermi surface.We expect the emergent neutral fermions that form a Fermi surface in the gapless QSL phase to show quantum oscillations in a magnetic field, similar to observations of quantum oscillations in SmB 6 , a topological Kondo insulator [50][51][52].…”

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confidence: 97%

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Magnetic field-induced intermediate quantum spin liquid with a spinon Fermi surface

Patel

Trivedi

2019

Proc. Natl. Acad. Sci. U.S.A.

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The Kitaev model with an applied magnetic field in the H||[111] direction shows two transitions: from a non-abelian gapped quantum spin liquid (QSL) to a gapless QSL at Hc1 0.2K and a second transition at a higher field Hc2 0.35K to a gapped partially polarized phase, where K is the strength of the Kitaev exchange interaction. We identify the intermediate phase to be a gapless U(1) QSL, and determine the spin structure function S(k) and the Fermi surface S F (k) of the gapless spinons using the density matrix renormalization group (DMRG) method for large honeycomb clusters. Further calculations of static spin-spin correlations, magnetization, spin susceptibility, and finite temperature specific heat and entropy, corroborate the gapped and gapless nature of the different field-dependent phases. In the intermediate phase, the spin-spin correlations decay as a power law with distance, indicative of a gapless phase.The inspired exact solution of the Kitaev model on a twodimensional honeycomb lattice with bond dependent spin exchange interaction [1] (Eq. 1) has emerged as a paradigmatic model for quantum spin liquids (QSL). For equal bond interactions (K), the ground state of the Kitaev model is known to be a topologically non-trivial gapless QSL with fractionalized excitations. The multiple ground state degeneracy reflects the topology of the lattice manifold (2-fold degeneracy on a cylinder and 4-fold degeneracy on a torus). The promise of utilizing fractionalized excitations for applications in robust quantum computing [1][2][3][4][5] has led to considerable excitement and activity in the field from diverse directions, all the way from fundamental developments to applications. Upon breaking time-reversal symmetry (TRS), for example by applying a magnetic field, the exact solvability of the Kitaev model is lost but perturbatively it can be shown that the Kitaev gapless QSL becomes a gapped QSL phase with non-abelian anyonic excitations [1].In order to realize the exotic properties of the Kitaev model, there has been keen interest to discover Kitaev physics in materials. To this end, Mott insulators with magnetic frustration and large spin-orbit coupling have been proposed [6], leading to the discovery of α-RuCl 3 and A 2 IrO 3 (A = Na, Li). These are candidate QSL materials with the desired honeycomb geometry. Although given additional interactions beyond the Kitaev interaction in materials, there is still controversy about the regimes where Kitaev physics can be accessed [7][8][9][10][11][12]. Additionally, triangular and Kagome lattice with spin frustration has also been proposed as a candidate for a QSL [13][14][15][16][17][18][19]. In this context, organics such as κ-(BEDT-TTF) 2 Cu 2 (CN) 3 [20] and EtMe 3 Sb[Pd(dmit) 2 ] 2 [21], the transition metal dichalcogenides 1T-TaS 2 [19] and a large family of rare-earth dichalcogenides AReX 2 (A = alkali or monovalent ions, Re = rare earth, X = O, S, Se) [22] have been explored. Remarkably, recent NMR and thermal Hall conductivity experiments on α-RuCl 3 demonstrate th...

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Section: Operators and Observablesmentioning

confidence: 99%

mentioning

confidence: 97%

Magnetic field-induced intermediate quantum spin liquid with a spinon Fermi surface

Patel

Trivedi

2019

Proc. Natl. Acad. Sci. U.S.A.

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“…We employ the DMRG correction-vector method throughout this paper [47]. Within the correction vector approach, we use the Krylov decomposition [48] rather than the conjugate gradient. An application of the method to Heisenberg and Hubbard ladders at half-filling can be found in Ref.…”

Section: B Dmrgmentioning

confidence: 99%

“…An application of the method to Heisenberg and Hubbard ladders at half-filling can be found in Ref. [67], while Ref. [68] presents a study of the pairing tendencies at finite hole-doping.…”

Section: B Dmrgmentioning

confidence: 99%

Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and FLEX results

Nocera¹,

Wang²,

Patel³

et al. 2018

Phys. Rev. B

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We study the magnetic and charge dynamical response of a Hubbard model in a two-leg ladder geometry using the density matrix renormalization group (DMRG) method and the random phase approximation within the fluctuation-exchange approximation (RPA+FLEX). Our calculations reveal that RPA+FLEX can capture the main features of the magnetic response from weak up to intermediate Hubbard repulsion for doped ladders, when compared with the numerically exact DMRG results. However, while at weak Hubbard repulsion both the spin and charge spectra can be understood in terms of weakly-interacting electron-hole excitations across the Fermi surface, at intermediate coupling DMRG shows gapped spin excitations at large momentum transfer that remain gapless within the RPA+FLEX approximation. For the charge response, RPA+FLEX can only reproduce the main features of the DMRG spectra at weak coupling and high doping levels, while it shows an incoherent character away from this limit. Overall, our analysis shows that RPA+FLEX works surprisingly well for spin excitations at weak and intermediate Hubbard U values even in the difficult low-dimensional geometry such as a two-leg ladder. Finally, we discuss the implications of our results for neutron scattering and resonant inelastic x-ray scattering experiments on two-leg ladder cuprate compounds.

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“…In principle, dynamic quantities are also accessible with the DMRG method [44][45][46] but at a high computational cost and with the additional complication of using pseudo-wave numbers and open boundary conditions (see Refs. [47,48] for recent works).…”

Section: B Qmcmentioning

confidence: 99%

Correlated atomic wires on substrates. II. Application to Hubbard wires

2017

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In the first part of our theoretical study of correlated atomic wires on substrates, we introduced lattice models for a one-dimensional quantum wire on a three-dimensional substrate and their approximation by quasi-one-dimensional effective ladder models [arXiv:1704.07350]. In this second part, we apply this approach to the case of a correlated wire with a Hubbard-type electronelectron repulsion deposited on an insulating substrate. The ground-state and spectral properties are investigated numerically using the density-matrix renormalization group method and quantum Monte Carlo simulations. As a function of the model parameters, we observe various phases with quasi-one-dimensional low-energy excitations localized in the wire, namely paramagnetic Mott insulators, Luttinger liquids, and spin-1/2 Heisenberg chains. The validity of the effective ladder models is assessed by studying the convergence with the number of legs and comparing to the full three-dimensional model. We find that narrow ladder models accurately reproduce the quasi-onedimensional excitations of the full three-dimensional model but predict only qualitatively whether excitations are localized around the wire or delocalized in the three-dimensional substrate.

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Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

Cited by 85 publications

References 47 publications

Magnetic field-induced intermediate quantum spin liquid with a spinon Fermi surface

Magnetic field-induced intermediate quantum spin liquid with a spinon Fermi surface

Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and FLEX results

Correlated atomic wires on substrates. II. Application to Hubbard wires

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