Erratum: Temperature-Induced Gap Formation in Dynamic Correlation Functions of the One-Dimensional Kondo Insulator: Finite-Temperature Density-Matrix Renormalization-Group Study [Phys. Rev. Lett. 81, 4939 (1998)]

Mutou, Tetsuya; Shibata, Naokazu; Ueda, Kazuo

doi:10.1103/physrevlett.82.3727

Cited by 14 publications

(22 citation statements)

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“…A very similar difference between the spin gap and the charge gap has been previously observed for many heavy fermion systems [8]. This difference has been explained by a few theoretical models, which predict that the spin gap is smaller than the charge gap [8,9]. Further details of this work may be found in [10].…”

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confidence: 63%

Study of the hybridization gap in a heavy fermion compound: CeRu4Sb12

Adroja

Park

McEwen

et al. 2004

Journal of Magnetism and Magnetic Materials

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supporting

confidence: 63%

Study of the hybridization gap in a heavy fermion compound: CeRu4Sb12

Adroja

Park

McEwen

et al. 2004

Journal of Magnetism and Magnetic Materials

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“…To confront the experimental findings on CuHpCl, we set J = 1, J ⊥ /J = 5.28. The TMRG technique we adopt here is implemented in the thermodynamic limit and can be used to evaluate very accurately the thermodynamic quantities [20,21] as well as imaginary time auto-correlation functions [22,23] at very low-T for quasi-1D systems. Technical aspects of this method can be found in Ref.…”

mentioning

confidence: 99%

Magnetic-Field Effects on Two-Leg Heisenberg Antiferromagnetic Ladders: Thermodynamic Properties

Wang

2000

Phys. Rev. Lett.

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Using the recently developed transfer-matrix renormalization group method, we have studied the thermodynamic properties of two-leg antiferromagnetic ladders in a magnetic field. Based on different magnetization behaviors, we found a disordered spin liquid, the Luttinger liquid, spin-polarized phases, and a classical regime. Our calculations in the Luttinger liquid regime suggest that both the divergence of the NMR relaxation rate and the anomalous specific heat behavior observed on Cu2(C5H12N2)2Cl4 are due to a quasi-one-dimensional effect rather than three-dimensional ordering.

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“…The combination of TMRG and maximum entropy has been used to calculate spectral functions for the XXZ-chain 10 and the Kondo-lattice model. 8 However, this method involves intrinsic errors due to the analytical continuation which cannot be resolved.…”

Section: 89mentioning

confidence: 99%

“…(6) has the same structure as the equation for the calculation of imaginary time CFs. 8,10 Only the transfer matrices involved are different. For practical DMRG calculations the parameters ǫ, δ are fixed and the temperature (time) is decreased (increased) by increasing M (N).…”

Section: 10mentioning

confidence: 99%

Real-time dynamics at finite temperature by the density-matrix renormalization group: A path-integral approach

Sirker

Klümper

2005

Phys. Rev. B

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We propose a path-integral variant of the DMRG method to calculate real-time correlation functions at arbitrary finite temperatures. To illustrate the method we study the longitudinal autocorrelation function of the XXZ-chain. By comparison with exact results at the free fermion point we show that our method yields accurate results up to a limiting time which is determined by the spectrum of the reduced density matrix. The density-matrix renormalization group (DMRG) 1 is today a well established numerical method to study ground state properties of one-dimensional quantum systems. Within the last few years the DMRG method has been generalized to allow also for the calculation of spectral functions 2 and, quite recently, to incorporate directly real-time evolution.3 The most powerful variant of DMRG to calculate thermodynamic properties is the density-matrix renormalization group applied to transfer matrices (TMRG). This method has been proposed by Bursill et al. 4 and has later been improved considerably. 5The main idea of TMRG is to express the partition function Z of a one-dimensional quantum model by that of an equivalent two-dimensional classical model obtained by a Trotter-Suzuki decomposition. 6 Thermodynamic quantities can then be calculated by considering a suitable transfer matrix T for the classical model. The main advantage of this method is that the thermodynamic limit (chain length L → ∞) can be performed exactly and that the free energy in the thermodynamic limit is determined solely by the largest eigenvalue of T . The TMRG has been applied to calculate static thermodynamic properties for a variety of one-dimensional systems including spin chains, the Kondo lattice model, the t − J chain and ladder, and also spin-orbital models. 7,8,9The Trotter-Suzuki decomposition of a onedimensional quantum system yields a two-dimensional classical model with one axis corresponding to imaginary time (inverse temperature). It is therefore straightforward to calculate imaginary-time correlation functions (CFs) using the TMRG algorithm. Although the results for the imaginary-time CFs obtained by TMRG are very accurate, the results for real-times (real-frequencies) involve large errors because the analytical continuation poses an ill-conditioned problem. In practice it has turned out that the maximum entropy method is the most efficient and reliable way to obtain spectral functions from TMRG data. The combination of TMRG and maximum entropy has been used to calculate spectral functions for the XXZ-chain 10 and the Kondo-lattice model. 8 However, this method involves intrinsic errors due to the analytical continuation which cannot be resolved.Here we propose a method to calculate directly realtime CFs at finite temperature by a modified TMRG algorithm thus avoiding an analytical continuation. We start by considering the two-point CF for an operator O r (t) at site r and time tTr (e −βH ) where ǫ = β/M so that the partition function Z = exp(−βH) becomes(3) With it → τ in Eq.(1) and inserting the identity operator at e...

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Erratum: Temperature-Induced Gap Formation in Dynamic Correlation Functions of the One-Dimensional Kondo Insulator: Finite-Temperature Density-Matrix Renormalization-Group Study [Phys. Rev. Lett. 81, 4939 (1998)]

Cited by 14 publications

References 0 publications

Study of the hybridization gap in a heavy fermion compound: CeRu4Sb12

Study of the hybridization gap in a heavy fermion compound: CeRu4Sb12

Magnetic-Field Effects on Two-Leg Heisenberg Antiferromagnetic Ladders: Thermodynamic Properties

Real-time dynamics at finite temperature by the density-matrix renormalization group: A path-integral approach

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