Haldane-gapped spin chains as Luttinger liquids: Correlation functions at finite field

This formalism is then applied to the study of ground state correlations of the Lieb-Liniger gas trapped in an external potential V(x)V(x). Relations with previous works on inhomogeneous Luttinger liquids are discussed. The main innovation here is in the identification of local observables \hat{O} (x)Ô(x) in the microscopic model with their field theory counterparts \partial_x h, e^{i h(x)}, e^{-i h(x)}∂xh,eih(x),e−ih(x), etc., which involve non-universal coefficients that themselves depend on position — a fact that, to the best of our knowledge, was overlooked in previous works on correlation functions of inhomogeneous Luttinger liquids —, and that can be calculated thanks to Bethe Ansatz form factors formulae available for the homogeneous Lieb-Liniger model. Combining those position-dependent coefficients with the correlation functions of the IGFF, ground state correlation functions of the trapped gas are obtained. Numerical checks from DMRG are provided for density-density correlations and for the one-particle density matrix, showing excellent agreement.

Download Full-text

Correlation Functions of Heisenberg Spin Chains : the Algebraic Bethe Ansatz Approach

10.22323/1.038.0008 ◽

2007 ◽

Author(s):

Jean-Michel Maillet

Keyword(s):

Bethe Ansatz ◽

Correlation Functions ◽

Spin Chains ◽

Heisenberg Spin ◽

Algebraic Bethe Ansatz ◽

Ansatz Approach ◽

Heisenberg Spin Chains

Download Full-text

Correlation functions of higher-dimensional Luttinger liquids

Physical Review B ◽

10.1103/physrevb.59.5377 ◽

1999 ◽

Vol 59 (8) ◽

pp. 5377-5383 ◽

Cited By ~ 9

Author(s):

Lorenz Bartosch ◽

Peter Kopietz

Keyword(s):

Correlation Functions ◽

Luttinger Liquids ◽

Higher Dimensional

Download Full-text

HEISENBERG INTEGER SPIN CHAINS IN A UNIFORM MAGNETIC FIELD

International Journal of Modern Physics B ◽

10.1142/s0217979202010099 ◽

2002 ◽

Vol 16 (09) ◽

pp. 1363-1379 ◽

Cited By ~ 8

Author(s):

L. CAMPOS VENUTI ◽

E. ERCOLESSI ◽

G. MORANDI ◽

P. PIERI ◽

M. RONCAGLIA

Keyword(s):

Magnetic Field ◽

Numerical Analysis ◽

Correlation Functions ◽

Uniform Magnetic Field ◽

Spin Chains ◽

Zero Temperature ◽

Heisenberg Chain ◽

Temperature Correlation ◽

Point Analysis ◽

External Uniform Magnetic Field

We investigate both numerically and analytically the behavior of a spin-1 antiferromagnetic isotropic Heisenberg chain in an external uniform magnetic field. Extensive DMRG studies of chains up to N = 80 sites extend previous analyses and obtain the zero-temperature correlation functions. We argue that, despite the presence of a magnetic field, the model is still well described by an O(3) nonlinear σ-model. A saddle-point analysis, that also includes Gaussian fluctuations, is developed for the latter both at zero and finite temperatures. Its predictions are compared with those of the numerical analysis and with the existing experimental literature.

Download Full-text