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arXiv:quant-ph/0509110 · Physica E Low-dimensional Systems and Nanostructures

Emergence of thermodynamic behavior within composite quantum systems

Günter Mahler A, Jochen Gemmer B, Mathias Michel A

Published Jul 2, 2005• 23 citations
arXivHTMLPDF
DOI
10.1016/j.physe.2005.05.001

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The physics of two-dimensional electron gas in a perpendicular magnetic field, i.e., the quantum Hall system, is remarkably rich. At half filling of the lowest Landau level, it has been predicted that "composite fermions"---emergent quasiparticles consisting of an electron attached to two magnetic flux quanta---experience zero net magnetic field and form a Fermi sea, dubbed composite Fermi liquid (CFL). However, despite its seemingly simple appearance, CFL is a strongly correlated quantum many-body state in disguise, and solving it in a controlled manner is extremely difficult, to the extent that the thermodynamic properties of CFL remain largely unknown. In this work, we perform state-of-the-art thermal tensor network simulations of the ν=1/2ν=1/2ν=1/2 Landau level system and observe low-temperature power-law behaviour of the specific heat, signaling the gapless nature of CFL. More importantly, the power is extracted to be close to 2/32/32/3, clearly deviating from the ordinary linear-TTT behaviour of Fermi liquid, suggesting coupling between the CFs and the dynamical emergent gauge field and thereby revealing the quantum many-body nature of the CFL state.
We describe the phase diagram and thermodynamic properties of a chain of axially-tunnel-coupled fractional quantum Hall systems realized by rotating a series of optical dipole traps about their center. We demonstrate not only a experimentally feasible pathway to a state describable as a Mott-insulator of composite bosons, but also describe the nature of the coherent states at higher tunnel coupling strength, and identify a series of new superfluid phases with rich behavior. The phase diagram directly reveals not only characteristic features of the few-body systems, including the effective mass of composite particle- and hole-like excitations and their interactions, but emergent properties of the chain also reveal a fundamental mapping between the adiabatic dynamics of two dimensional systems governed by particle braiding and the hydrostatic response of the gas in the conducting phases.