Phase diagram and correlation exponents for interacting fermions in one dimension

Journal Article · Mon Jan 01 04:00:00 EST 1996 · Reviews of Modern Physics

DOI:https://doi.org/10.1103/RevModPhys.68.175· OSTI ID:282941

Kolomeisky, E B ^[1]; Straley, J P ^[2]

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1. Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853-2501 (United States)
2. Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506-0055 (United States)

A theory is given for the ground-state properties of short-ranged interacting spin-1/2 fermions moving in a periodic potential, based on a combination of renormalization-group ideas, the harmonic (Luttinger) liquid approach, and the symmetry properties of the Hubbard model, for a wide range of interactions and arbitrary fillings. For rational filling factors the outcome depends nontrivially on the parity of the order of the 2{ital k}{sub {ital F}} umklapp scattering: even values fall into a universality class characterized by a separation of charge and spin degrees of freedom in the long-wavelength limit, while the action for the case of odd orders does not have this property, thus leading to distinct phase diagrams. It is argued that even when the long-wavelength action does exhibit a spin-charge separation it is not always an accurate approximation, particularly for the case of strong repulsion between electrons of the same spin. This leads to a classification of the possible ground states, associated correlation exponents, and phase transitions. The translational correlation exponents upon approaching insulator phases (existing at exact commensuration) by changing electron density can be related to the fractional charge of the solitons, using the Landauer rule. {copyright} {ital 1996 The American Physical Society.}

• OSTI ID: 282941
• Journal Information: Reviews of Modern Physics, Journal Name: Reviews of Modern Physics Journal Issue: 1 Vol. 68; ISSN 0034-6861; ISSN RMPHAT
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
COMMENSURATE-INCOMMENSURATE TRANSFORMATIONS
CORRELATION FUNCTIONS
ELECTRON GAS
FERMIONS
GROUND STATES
HUBBARD MODEL
ONE-DIMENSIONAL SYSTEMS
PHASE TRANSFORMATIONS
RENORMALIZATION
SPIN