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Acta Physica Polonica A

Pairing Scenarios for the Hubbard Model in the Strong Coupling Limit

Vardan Apinyan, T. K. Kopeć

Published Jul 1, 2008• 0 citations
Publisher

Abstract

We consider a spin-rotationally invariant Hubbard model.The original electron operator is presented in the charge-spin-fermion U(1)×SU(2) factorized form.The factorization procedure is given in terms of the emergent gauge fields.As a result, the electron appears like a composite object consisting of strongly fluctuating phase field and spatially rotating spin axis.Furthermore, we elaborate microscopically on the form of possible pairing states.

DOI
10.12693/aphyspola.114.159

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We consider a spin-rotationally invariant Hubbard model.The original electron operator is presented in the charge-spin-fermion U(1)×SU(2) factorized form.The factorization procedure is given in terms of the emergent gauge fields.As a result, the electron appears like a composite object consisting of strongly fluctuating phase field and spatially rotating spin axis.Furthermore, we elaborate microscopically on the form of possible pairing states.
We implement the rotationally invariant formulation of the two-dimensional Hubbard model, with nearest-neighbors hopping ttt, which allows for the analytical study of the system in the low-energy limit. Both U(1) and SU(2) gauge transformations are used to factorize the charge and spin contributions to the original electron operator in terms of the corresponding gauge fields. The Hubbard Coulomb energy UUU term is then expressed in terms of quantum phase variables conjugate to the local charge and variable spin-quantization axis, providing a useful representation of strongly correlated systems. It is shown that these gauge fields play a similar role as phonons in the BCS theory: they act as the ``glue'' for fermion pairing. By tracing out gauge degrees of freedom, the form of paired states is established and the strength of the pairing potential is determined. It is found that the attractive pairing potential in the effective low-energy fermionic action is nonzero in a rather narrow range of U/tU/tU/t.
The spin-rotationally invariant SU(2) approach to the Hubbard model is extended to accommodate the charge degrees of freedom. Both U(1) and SU(2) gauge transformation are used to factorize the charge and spin contribution to the original electron operator in terms of the emergent gauge fields. It is shown that these fields play a similar role as phonons in the BCS theory; they provide the ``glue'' for fermion pairing. By tracing out gauge bosons the form of paired states is established and the role of antiferromagnetic correlations is explicated.
The spin-rotationally invariant SU(2) approach to the Hubbard model is extended to accommodate the charge degrees of freedom.Both U(1) and SU(2) gauge transformation are used to factorize the charge and spin contribution to the original electron operator in terms of the emergent gauge fields.It is shown that these fields play a similar role as phonons in the BCS theory: they provide the "glue" for fermion pairing.By tracing out gauge bosons the form of paired states is established and the role of antiferromagnetic correlations is explicated.
Abstract A spin‐charge unifying description for the Hubbard model based on the time dependent local gauge transformations is developed. The collective variables for charge and spin are isolated in the form of the space‐time fluctuating U(1) phase field and rotating spin quantization axis governed by the SU(2) symmetry, respectively. As a result interacting electrons appear as a composite objects consisting of bare fermions with attached U(1) and SU(2) gauge fields. We elaborate on the microscopic origins of the effective action with the Coulomb interaction that contain topological theta terms. Furthermore, we unravel the link between non‐trivial multiply‐connected topological structure of the U(2) = U(1) ⊗ SU(2) configurational space for gauge fields and the instanton contribution to the statistical sum. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Abstract We implement the rotationally invariant formulation of the two‐dimensional Hubbard model, with nearest‐neighbors hopping t, which allows for the analytic study of the system in the low‐energy limit. Both U(1) and SU(2) gauge transformation are used to factorize the charge and spin contribution to the original electron operator in terms of the corresponding gauge fields. The Hubbard Coulomb energy U‐term is then expressed in terms of quantum phase variables conjugate to the local charge and variable spin quantization axis, providing a useful representation of strongly correlated systems. It is shown that these gauge fields play a similar role as phonons in the BCS theory: they act as the “glue” for fermion pairing.
The spin-rotationally invariant SU(2)×U(1) approach to the Hubbard model is extended to accommodate the charge degrees of freedom.Both U(1) and SU(2) gauge transformation are used to factorize the charge and spin contribution to the original electron operator in terms of the emergent gauge elds.By tracing out gauge bosons the form of paired states is established and the role of antiferromagnetic correlations is explicated.We argue that in strongly correlated electron system collective instanton excitations of the phase eld (dual to the charge) arise with a great degree of stability, governed by gauge ux changes by an integer multiple of 2π.Furthermore, it is shown that U(1) and SU(2) gauge elds play a similar role as phonons in the BCS theory: they act as the the "glue" for fermion pairing.