Finite-size corrections and numerical calculations for long spin 1/2 Heisenberg chains in the critical region

Woynarovich, F.; Eckle, Hans-Peter

doi:10.1088/0305-4470/20/2/010

Cited by 197 publications

(121 citation statements)

References 14 publications

Supporting

Mentioning

113

Contrasting

Order By: Relevance

“…confirming the field theoretical prediction in [28] about the amplitude of the 1/(log T ) 3 correction which was argued to be universal however in disagreement with Bethe ansatz calculations in [27]. The reason for the "failure" of the treatment in [27] (instead of [12,13,14] were still plagued by higher order logarithmic contributions leading to erroneous conclusions with respect to the analysis of the specific heat.…”

Section: Asymptotics Of the Specific Heatsupporting

confidence: 56%

“…The reason for the "failure" of the treatment in [27] (instead of [12,13,14] were still plagued by higher order logarithmic contributions leading to erroneous conclusions with respect to the analysis of the specific heat. For an illustration of these higher order terms see Fig.…”

Section: Asymptotics Of the Specific Heatmentioning

confidence: 99%

“…In the same way as (27) defines a function ρ for the inhomogeneity ρ 0 , it gives rise to the dressed energy ǫ(x) and the dressed charge ξ(x) related to (31). (Note that the auxiliary function a(x) of the thermodynamic treatment is related to ǫ(x) in the lowtemperature limit via log a = βǫ and (3) turns into the linear integral equation for the dressed energy.)…”

Section: Bulk Propertiesmentioning

confidence: 99%

“…The main results concern the numerical and analytical calculation of the universal leading and next-leading corrections in the susceptibility. In particular the resolution of a controversy between exact [27], field theoretical [28] and numerical approaches [12,13,14,29] about the specific heat at low temperatures is presented which is absolutely free of fitting procedures in the analysis of the zero-temperature limit. Our approach permits the numerical study of extremely low-temperatures down to T /J = 10 −24 .…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents

1998

View full text Add to dashboard Cite

We present numerical and analytical results for the thermodynamical properties of the spin-1/2 Heisenberg chain at arbitrary external magnetic field. Special emphasis is placed on logarithmic corrections in the susceptibility and specific heat at very low temperatures (T /J = 10 −24 ) and small fields. A longstanding controversy about the specific heat is resolved. At zero temperature the spin-Peierls exponent is calculated in dependence on the external magnetic field. This describes the energy response of the system to commensurate and incommensurate modulations of the lattice. The exponent for the spin gap in the incommensurate phase is given.

show abstract

Section: Asymptotics Of the Specific Heatsupporting

confidence: 56%

Section: Asymptotics Of the Specific Heatmentioning

confidence: 99%

Section: Bulk Propertiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents

1998

View full text Add to dashboard Cite

show abstract

“…] is the Luttinger parameter [35]. Thus, for the non-interacting case g = 1 and ξ MP = ξ while for U = −1, g = 3/2 and ξ MP diverges.…”

mentioning

confidence: 97%

Entanglement entropy of low-lying excitation in localized interacting system: Signature of Fock space delocalization

Berkovits

2014

Phys. Rev. B

View full text Add to dashboard Cite

The properties of the entanglement entropy (EE) of low-lying excitations in one-dimensional disordered interacting systems are studied. The ground state EE shows a clear signature of localization, while low-lying excitation shows a crossover from metallic behavior at short sample sizes to localized at longer length. The dependence of the crossover as function of interaction strength and sample length is studied using the density matrix renormalization group (DMRG). This behavior corresponds to the presence of the predicted many particle critical energy in the vicinity of the Fermi energy. Implications of these results to experiments are discussed. PACS numbers: 73.20.Fz,03.65.Ud,71.10.Pm,73.21.Hb Many body localization (MBL) has drawn growing interest in recent years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The Anderson localization transition [21,22] is a zero-temperature quantum phase transition, which for the non-interacting case is manifested in the properties of the single-particle eigenstates and eigenvalues [23]. For one and two dimensional systems all the single-particle state are localized for any amount of disorder, while for three dimensional systems at a given disorder there exists a critical energy (mobility edge) below which all states are localized. For a many-particle system, as long as no particleparticle interactions are present, the properties of a many-particle excited state are determined by the properties of the single-particle states. Thus, as long as all the particles occupy localized single-particle states the manyparticle states should exhibit localized behavior. For example, the entanglement entropy (EE) between any subregion A of the system and the rest of it should saturate (i.e., S A ∝ ξ d−1 , where d is the dimensionality of the system and ξ is the single-electron localization length). While if some of the extended single-particle states are occupied the usual volume law for the EE (S A ∝ L d A , where L A is the length of region A) is observed [17]. Physically, the difference between the localized and extended many-particle states is manifested in the dynamics of a particle tunneling into some particular region of the system, or a particle excited by a confined external perturbation in the region. In the localized phase it will remain there (i.e., will have a very long lifetime -sharp level), while in the extended case it will leave the region (short lifetime -broad level).What is the influence of particle-particle interaction on the above picture? A cursory consideration may lead to the conclusion that since particles now interact with each other, any localized excitation will eventually spread all over the system. Thus, the rest of the system acts as a thermal bath for any excited sub-system [24][25][26]. Surprisingly, Basko, Aleiner and Altshuler [2] have shown that if all the single-electron states are localized, an excitation will remain localized even in the presence of particleparticle interactions up to a critical temperature or excitatio...

show abstract

Quantum spin chains with various defects

Schuster¹,

Eckern²

2002

Ann. Phys.

View full text Add to dashboard Cite

Using the density matrix renormalization group (DMRG) method, we study the quantum coherence in one-dimensional disordered spin chains and Fermi systems. We consider in detail spinless fermions on a ring, and compare the influence of several kinds of impurities in a gapless and a dimerized, gapped system. In the translation-invariant system a so-called site-impurity, which can be realized by a local potential or a modification of one link, increases for repulsive interaction, and decreases for attractive interaction, upon renormalization. The weakening of two neighbouring bonds, which is a realization of a socalled bond-impurity, on the other hand, is healed for repulsive interaction, but enhanced for intermediate attractive interactions. This leads to a strong suppression of the quantum coherence measured by the phase sensitivity, but not to localization. Adding a local distortion to a dimerized system, we find that even the presence of a single site-impurity increases the metallic region found in the dimerized model. For a strong dimerization and a high barrier, an additional sharp maximum, is seen in the phase sensitivity as a function of interaction, already for systems with about 100 sites. A bond-impurity in the dimerized system also opens a small metallic window in the otherwise isolating regime.

show abstract

Finite-size corrections and numerical calculations for long spin 1/2 Heisenberg chains in the critical region

Cited by 197 publications

References 14 publications

The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents

The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents

Entanglement entropy of low-lying excitation in localized interacting system: Signature of Fock space delocalization

Quantum spin chains with various defects

Contact Info

Product

Resources

About