Quantum Criticality and the Kondo Lattice

Giamarchi, Thierry

doi:10.1201/b10273-15

Cited by 5 publications

(8 citation statements)

References 34 publications

(56 reference statements)

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“…where (using the notation of [2,10]) ∂ x φ denotes fluctuations of the magnetization in the z direction, θ is the con-…”

Section: Model and Methodsmentioning

confidence: 99%

“…Qualitatively, our theory might explain dips at B ∼ T observed in recent heat transport measurements on copper pyrazine dinitrate, but a fully quantitative description is not possible within our model. Some of the most fascinating manifestations of quantum many-body physics in one-dimension (1D) can be found in spin- 1 2 chain systems 1,2 . In particular, the spin- 1 2 Heisenberg model with antiferromagnetic nearest neighbor exchange interactions is one of the most extensively studied paradigms.…”

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confidence: 99%

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Large thermomagnetic effects in weakly disordered Heisenberg chains

et al. 2009

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The interplay of different scattering mechanisms can lead to novel effects in transport. We show theoretically that the interplay of weak impurity and Umklapp scattering in spin-1/2 chains leads to a pronounced dip in the magnetic field dependence of the thermal conductivity $\kappa$ at a magnetic field $B \sim T$. In sufficiently clean samples, the reduction of the magnetic contribution to heat transport can easily become larger than 50% and the effect is predicted to exist even in samples with a large exchange coupling, J >> B, where the field-induced magnetization is small. Qualitatively, our theory might explain dips at $B \sim T$ observed in recent heat transport measurements on copper pyrazine dinitrate, but a fully quantitative description is not possible within our model.Comment: 5 pages, 2 figure

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“…where (using the notation of [2,10]) ∂ x φ denotes fluctuations of the magnetization in the z direction, θ is the con-…”

Section: Model and Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

Large thermomagnetic effects in weakly disordered Heisenberg chains

et al. 2009

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“…Spin-1/2 quasi-one-dimensional (Q1D) magnets are ideal candidates for observing fundamental quantum phenomena as the combination of low dimensionality and small spin-magnitude maximizes quantum fluctuations [2,3]. This has motivated experimentalists for many decades to realize one dimensional quantum magnets [4,5].…”

Section: Introductionmentioning

confidence: 99%

Cluster mean-field study of the Heisenberg model for CuInVO5

Singhania

Kumar

2018

Phys. Rev. B

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Motivated by the experimental report of unusual low temperature magnetism in quasi onedimensional magnet CuInVO5, we present results of a cluster mean-field study on a spin-1/2 Heisenberg model with alternating ferromagnetic and antiferromagnetic nearest-neighbor coupling. We map out the ground state phase diagrams with varying model parameters, including the effect of an external magnetic field. An unexpected competition between different spin-spin correlations is uncovered. Multiple spin-flop transitions are identified with the help of component resolved correlation functions. For the material-specific choice of model parameters we discuss the temperature dependence of specific heat and magnetic susceptibility, and compare our results with the available experimental data. A detailed account of spin-spin correlations allows us to present a microscopic understanding of the low-temperature magnetic ordering in CuInVO5. Most notably, we identify the origin of an extra peak in the low temperature specific heat data of CuInVO5 reported by Hase et al. [1]. PACS numbers: 75.10.-b, 75.10.Pq, 75.40.Cx 1 2 3 4 J 2 J 2 J 1 J 3 FIG. 1. (Color online) A schematic picture of the coupled tetramer model. Each dot represents a spin-1/2 and the nearest-neighbor couplings are indicated by double (J1), solid (J2) and dotted (J3) lines.

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“…They are for instance susceptible to a lattice when they can form a Mott insulator or to disorder when they can form a Bose glass [2]. A particular kind of relevant perturbations are the ones leading to a dimensional crossover in which Luttinger liquids or 1d systems are coupled with each other in a matrix of higher dimension [3], which can be experimentally realized [4,5]. We will consider hopping processes (that is, a Josephson coupling) between tubes of scalar bosonic Luttinger liquids and Mott insulators arranged in a 2d setup, where the intertube coupling is varied from zero to an equally strong value as the intra-tube coupling.…”

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confidence: 99%

“…We will consider hopping processes (that is, a Josephson coupling) between tubes of scalar bosonic Luttinger liquids and Mott insulators arranged in a 2d setup, where the intertube coupling is varied from zero to an equally strong value as the intra-tube coupling. For this 1d-2d crossover, mean-field theory fails [6][7][8], and this topic is one of the remaining open problems in the 1d world [3,9].…”

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Ground-state phase diagram of the two-dimensional Bose-Hubbard model with anisotropic hopping

Schönmeier-Kromer

Pollet

2014

Phys. Rev. A

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We compute the ground state phase diagram of the 2d Bose-Hubbard model with anisotropic hopping using quantum Monte Carlo simulations, connecting the 1d to the 2d system. We find that the tip of the lobe lies on a curve controlled by the 1d limit over the full anisotropy range while the universality class is always the same as in the isotropic 2d system. This behavior can be derived analytically from the lowest RG equations and has a shape typical for the underlying Kosterlitz-Thouless transition in 1d. We also compute the phase boundary of the Mott lobe at unit density for strong anisotropy and compare it to the 1d system. Our calculations shed light on recent cold gas experiments monitoring the dynamics of an expanding cloud.PACS numbers: 03.75. Hh, 64.70.Tg, 05.30.Jp In one dimension, interactions and quantum fluctuations are stronger than in any other dimension. As a consequence, single-particle excitations cannot occur and only collective excitations are formed. The liquids in 1d are known as Luttinger liquids [1], which are critical phases with algebraic correlations. They are for instance susceptible to a lattice when they can form a Mott insulator or to disorder when they can form a Bose glass [2]. A particular kind of relevant perturbations are the ones leading to a dimensional crossover in which Luttinger liquids or 1d systems are coupled with each other in a matrix of higher dimension [3], which can be experimentally realized [4,5]. We will consider hopping processes (that is, a Josephson coupling) between tubes of scalar bosonic Luttinger liquids and Mott insulators arranged in a 2d setup, where the intertube coupling is varied from zero to an equally strong value as the intra-tube coupling. For this 1d-2d crossover, mean-field theory fails [6][7][8], and this topic is one of the remaining open problems in the 1d world [3,9].Recently, studies on dimensional crossovers for fermions have come to the front of attention again. The Mott transition in a frustrated Hubbard model with nextnearest neighbor hopping at half filling on a quasi 1d lattice was studied in Ref.[10], featuring a closing of the 1d Mott gap and supporting the idea that superconductivity is mediated by magnetic fluctuations in organic salts [11]. The situation is reminiscent of the pseudogap phase in high-T c cuprates where enhanced spin fluctuations and spatial correlations in the copper oxide planes occur in the proximity of an insulating phase. The study was extended to dynamical correlation functions in Ref.[12] providing evidence for a dimensional-crossoverdriven confinement of spinons [13]. A 3d Hubbard model with anisotropic hopping was studied with cluster dynamical mean field methods and yielded results in agreement with a cold gas realization for temperatures down to the hopping amplitude [14].In a recent cold gas experiment by Ronzheimer et al.[15] a bosonic system was prepared in the atomic limit in 2d with precisely one particle per site. The experimentalists then quenched the interaction and the hopping along the x and ...

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Quantum Criticality and the Kondo Lattice

Cited by 5 publications

References 34 publications

Large thermomagnetic effects in weakly disordered Heisenberg chains

Large thermomagnetic effects in weakly disordered Heisenberg chains

Cluster mean-field study of the Heisenberg model for CuInVO5

Ground-state phase diagram of the two-dimensional Bose-Hubbard model with anisotropic hopping

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