# Breaking an Electron: Spin Incoherent Behavior in Strongly Correlated Low Dimensional Systems

**When:**Thursday, March 22, 2012 at 4:00 pm

**Where:**DA 114

**Speaker**: Adrian Feiguin

**Organization**: University of Wyoming

**Sponsor**: Physics Colloquium

Electrons are fundamental building blocks of nature and are indivisible in isolation. However, when electrons (or other quantum particles with an internal “spin” degree of freedom) are confined in one spatial dimension, they may loose their identity as individual particles, and “break” into separate excitations carrying spin, and charge, with each degree of freedom being characterized by a different energy scale. While the basic theoretical understanding of spin-charge separation in one-dimension, known as “Luttinger liquid theory”, has existed for some time, recently a previously unidentified regime of strongly interacting one-dimensional systems at finite temperature came to light: The “spin-incoherent Luttinger liquid”. This occurs when the temperature is larger than the characteristic spin energy scale. The key to establishing both Luttinger liquid behavior and spin-incoherent Luttinger liquid behavior in experiment is detailed knowledge of the spectral properties.

I will present a numerical study of the finite-temperature properties of a one-dimensional fermionic gas in the spinincoherent regime using the time-dependent density matrix renormalization group method. This approach enables us to quantitatively handle the experimentally relevant and theoretically challenging “crossover” regime between the Luttinger liquid and spin-incoherent Luttinger liquid limits. I will introduce a framework based on the so-called “thermo-field” formalism, that allows one to describe a thermally mixed state as a pure state in an enlarged Hilbert space. In this language a thermal average reduces to a regular quantum mechanical one. I will show that the spin-incoherent state can be described exactly as a generalization of the Bethe Ansatz solution –the Ogata and Shiba’s factorized wave function– in an enlarged Hilbert space.

Finally, I will discuss the possibility of realizing spin-incoherent behavior in the *ground-state* of model Hamiltonians, such as ladders, and the Kondo lattice, where “temperature” is parametrized by an interaction term in the problem.

References:

A. E. Feiguin and G. Fiete, Phys. Rev. Lett. 106, 146401 (2011) and Phys. Rev. B 81, 075108 (2010)