Thermodynamics and excitations of the one-dimensional Hubbard model

Deguchi, Tetsuo; Eßler, Fabian H. L.; Göhmann, Frank; Klümper, Andreas; Korepin, V. E.; Kusakabe, Koichi

doi:10.1016/s0370-1573(00)00010-7

Cited by 58 publications

(26 citation statements)

References 103 publications

(369 reference statements)

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“…We are considering an Hamiltonian of the form However, it is also clear that the general task of solving the Lieb-Wu equations for all states in the perturbative multiplet and fixed L (possibly large) is not easy [32]. However, there are exceptions.…”

Section: Direct Analysis Of the Lieb-wu Equationsmentioning

confidence: 99%

Strong coupling anomalous dimensions of Script N = 4 super Yang-Mills

Beccaria¹,

Ortix²

2006

J. High Energy Phys.

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We study the strong coupling behaviour of fixed length single trace operators in the scalar SU(2) sector of N = 4 SYM. We assume the recently proposed connection with a twisted half-filled Hubbard model. By explicit direct diagonalization of operators with length L = 4, 6, 8 we study the full perturbative multiplet of those lattice states which have a clear correspondence with gauge theory composite operators. For this multiplet, we follow the weak-strong coupling flow to free fermion states and identify in particular the precise asymptotic fermion configuration. Next, we analyze the Lieb-Wu equations of the twisted Hubbard model. For the antiferromagnetic state we derive its strong coupling expansion working at L up to 32. We also study the lightest state in the perturbative multiplet. This state is non trivial since involves complex solutions of the Lieb-Wu equations. It is particularly interesting for AdS 5 × S 5 duality since it is dual to the folded string semiclassical solution in the thermodynamical limit. We are able to perform the full analysis and compute the next-to-next-to leading terms in the strong coupling expansion for the non trivial lengths L = 12 and L = 20. A general formula is proposed for the NLO expansion for any L = 4(2k + 1), k ∈ N.

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Section: Direct Analysis Of the Lieb-wu Equationsmentioning

confidence: 99%

Strong coupling anomalous dimensions of Script N = 4 super Yang-Mills

Beccaria¹,

Ortix²

2006

J. High Energy Phys.

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“…The effective parameters λ and µ can be related to the original parameters through a renormalization group, but here we do not need explicit relations. Since there is no spin-dependent coupling, the Hamiltonian has U(2) symmetry in which we can use the Bethe ansatz technique [28,35]. The resultant Bethe ansatz equations are [36,37] (See appendix B)…”

Section: Quantum Exact Gapless Modesmentioning

confidence: 99%

Quantum exact non-abelian vortices in non-relativistic theories

Nitta

Uchino

Vinci

2014

J. High Energ. Phys.

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Non-Abelian vortices arise when a non-Abelian global symmetry is exact in the ground state but spontaneously broken in the vicinity of their cores. In this case, there appear (non-Abelian) Nambu-Goldstone (NG) modes confined and propagating along the vortex. In relativistic theories, the Coleman-Mermin-Wagner theorem forbids the existence of a spontaneous symmetry breaking, or a long-range order, in 1+1 dimensions: quantum corrections restore the symmetry along the vortex and the NG modes acquire a mass gap. We show that in non-relativistic theories NG modes with quadratic dispersion relation confined on a vortex can remain gapless at quantum level. We provide a concrete and experimentally realizable example of a three-component Bose-Einstein condensate with U(1) × U(2) symmetry. We first show, at the classical level, the existence of S 3 S 1 S 2 (S 1 fibered over S 2 ) NG modes associated to the breaking U(2) → U(1) on vortices, where S 1 and S 2 correspond to type I and II NG modes, respectively. We then show, by using a Bethe ansatz technique, that the U(1) symmetry is restored, while the SU(2) symmery remains broken non-pertubatively at quantum level. Accordingly, the U(1) NG mode turns into a c = 1 conformal field theory, the Tomonaga-Luttinger liquid, while the S 2 NG mode remains gapless, describing a ferromagnetic liquid. This allows the vortex to be genuinely non-Abelian at quantum level.

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“…Fortunately, the 1D Hubbard model belongs to this class of systems and can be solved using the nested Bethe ansatz [12]. At zero temperature a relatively large body of knowledge has been accumulating steadily in-cluding: elementary excitations [13][14][15][16][17][18][19][20][21], complete set of eigenstates [22], magnetic properties [23][24][25][26], symmetries [27][28][29][30] and correlation functions .…”

Section: Introductionmentioning

confidence: 99%

Quantum critical behavior and thermodynamics of the repulsive one-dimensional Hubbard model in a magnetic field

2020

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Even though the Hubbard model is one of the most fundamental models of highly correlated electrons, analytical and numerical data describing its thermodynamics at nonzero magnetization are relatively scarce. We present a detailed investigation of the thermodynamic properties for the one dimensional repulsive Hubbard model in the presence of an arbitrary magnetic field for all values of the filling fraction and temperatures as low as T ∼ 0.005 t. Our analysis is based on the system of integral equations derived in the quantum transfer matrix framework. We determine the critical exponents of the quantum phase transitions and also provide analytical derivations for some of the universal functions characterizing the thermodynamics in the vicinities of the quantum critical points. Extensive numerical data for the specific heat, susceptibility, compressibility, and entropy are reported. The experimentally relevant double occupancy presents an interesting doubly nonmonotonic temperature dependence at intermediate values of the interaction strength and also at large repulsion and magnetic fields close to the critical value. The susceptibility in zero magnetic field has a logarithmic singularity at low temperatures for all filling factors similar to the behavior of the same quantity in the XXX spin chain. We determine the density profiles for a harmonically trapped system and show that while the total density profile seems to depend mainly on the value of chemical potential at the center of the trap the distribution of phases in the inhomogeneous system changes dramatically as we increase the magnetic field.

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Thermodynamics and excitations of the one-dimensional Hubbard model

Cited by 58 publications

References 103 publications

Strong coupling anomalous dimensions of Script N = 4 super Yang-Mills

Strong coupling anomalous dimensions of Script N = 4 super Yang-Mills

Quantum exact non-abelian vortices in non-relativistic theories

Quantum critical behavior and thermodynamics of the repulsive one-dimensional Hubbard model in a magnetic field

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