scholarly journals Correlation functions of higher-dimensional Luttinger liquids

1999 ◽  
Vol 59 (8) ◽  
pp. 5377-5383 ◽  
Author(s):  
Lorenz Bartosch ◽  
Peter Kopietz
Keyword(s):  
Correlation Functions ◽  
Luttinger Liquids ◽  
Higher Dimensional

scholarly journals The Inhomogeneous Gaussian Free Field, with application to ground state correlations of trapped 1d Bose gases

2018 ◽  
Vol 4 (6) ◽  
Author(s):  
Yannis Brun ◽  
Jerome Dubail
Keyword(s):  
Ground State ◽  
Correlation Functions ◽  
Particle Density ◽  
Free Field ◽  
Form Factors ◽  
Gaussian Free Field ◽  
Luttinger Liquids ◽  
Model Combining ◽  
Ground State Correlation ◽  
Trapped Gas

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.

scholarly journals SOME EXPERIMENTAL TESTS OF TOMONAGA–LUTTINGER LIQUIDS

2012 ◽  
Vol 26 (22) ◽  
pp. 1244004 ◽  
Author(s):  
T. GIAMARCHI
Keyword(s):  
Fermi Liquid ◽  
Luttinger Liquid ◽  
Experimental Tests ◽  
Spin Systems ◽  
One Dimension ◽  
Luttinger Liquids ◽  
One Dimensional ◽  
Higher Dimensional ◽  
Made In

The Tomonaga–Luttinger–Liquid (TLL) has been the cornerstone of our understanding of the properties of one dimensional systems. This universal set of properties plays in one dimension, the same role than Fermi liquid plays for the higher dimensional metals. I will give in these notes an overview of some of the experimental tests that were made to probe such TLL physics. In particular I will detail some of the recent experiments that were made in spin systems and which provided remarkable quantitative tests of the TLL physics.

A short proof of the McCoy conjecture in higher-dimensional classical continuous models of Kac types

2017 ◽  
Vol 31 (10) ◽  
pp. 1750111 ◽  
Author(s):  
Assane Lo
Keyword(s):  
Phase Transitions ◽  
Correlation Functions ◽  
Short Proof ◽  
Higher Dimensional ◽  
Continuous Models ◽  
Higher Derivatives ◽  
Derivatives Of

We consider the pressure and correlation functions of d-dimensional classical continuous models of Kac type. We prove that if the kth moments of the potential exist, then the system cannot have phase transitions of order lower than k. We also obtain a better formula for the higher derivatives of the pressure that leads to more precise estimates of the truncated correlations.

FORMAL CONSTRAINTS ON SERIES ANALYSIS ON THE POTTS MODEL

1987 ◽  
Vol 01 (04) ◽  
pp. 145-153 ◽  
Author(s):  
D. HANSEL ◽  
J.M. MAILLARD
Keyword(s):  
Magnetic Field ◽  
Partition Function ◽  
Low Temperature ◽  
Potts Model ◽  
Correlation Functions ◽  
Exact Results ◽  
Nearest Neighbour ◽  
Temperature Expansion ◽  
Higher Dimensional ◽  
Formal Constraints

It is shown that the low temperature expansion of the partition function, magnetization and nearest neighbour correlation functions of the q-state checkerboard Potts model in a magnetic field drastically simplify on a very simple algebraic variety. These four formal constraints on the expansions are also analysed in the framework of the resummed low temperature expansions and the large q expansions. These exact results are generalized straightforwardly to higher dimensional hypercubic lattices and also to some random problems.

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