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Acta Physica Polonica A

Magnetically Driven Superconducting Pairing Interaction in the Two-Dimensional Hubbard Model within a Spin-Rotationally Invariant Approach

Vardan Apinyan, T. K. Kopeć

Published Aug 1, 2010• 0 citations
Publisher

Abstract

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.

DOI
10.12693/aphyspola.118.273

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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.
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.
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.
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 antiferromagnetic phase of two-dimensional (2D) and three-dimensional (3D) Hubbard model with nearest neighbor hopping is studied on a bipartite cubic lattice by means of the quantum $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ rotor approach that yields a fully self-consistent treatment of the antiferromagnetic state that respects the symmetry properties of the model and satisfy the Mermin-Wagner theorem. 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 composite objects consisting of bare fermions with attached U(1) and SU(2) gauge fields. An effective action consisting of a spin-charge rotor and a fermionic field is derived as a function of the Coulomb repulsion UUU and hopping parameter ttt. At zero temperature, our theory describes the evolution from a Slater (U⪡t)(U⪡t)(U⪡t) to a Mott-Heisenberg (U⪢t)(U⪢t)(U⪢t) antiferromagnet. The results for zero-temperature sublatice magnetization (2D) and finite temperature (3D) phase diagram of the antiferromagnetic Hubbard model as a function of the crossover parameter U∕tU∕tU∕t are presented and the role of the spin Berry phase in the interaction driven crossover is analyzed.