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arXiv:1802.10553 · Physical review. B./Physical review. B

Topological phase transition in a two-species fermion system: Effects of a rotating trap potential or a synthetic gauge field

Shiuan-Fan Liou, Zi-Xiang Hu, Kun Yang

Published Jun 25, 2018• 1 citation
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Abstract

We numerically investigate the quantum phases and phase transition in a system made of two species of fermionic atoms that interact with each other via $s$-wave Feshbach resonance and are subject to rotation or a synthetic gauge field that puts the fermions at Landau level filling factor ${\ensuremath{\nu}}_{f}=2$. We show that the system undergoes a continuous quantum phase transition from a ${\ensuremath{\nu}}_{f}=2$ fermionic integer quantum Hall state formed by atoms to a ${\ensuremath{\nu}}_{b}=1/2$ bosonic fractional quantum Hall state formed by bosonic diatomic molecules. In the disk geometry we use, these two different topological phases are distinguished by their different gapless edge excitation spectra, and the quantum phase transition between them is signaled by the closing of the energy gap in the bulk. Comparisons will be made with field-theoretical predictions and the case of $p$-wave pairing.

DOI
10.1103/physrevb.97.245140

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We numerically investigate the quantum phases and phase transition in a system made of two species of fermionic atoms that interact with each other via sss-wave Feshbach resonance and are subject to rotation or a synthetic gauge field that puts the fermions at Landau level filling factor \ensuremathνf=2{\ensuremath{\nu}}_{f}=2\ensuremathνf​=2. We show that the system undergoes a continuous quantum phase transition from a \ensuremathνf=2{\ensuremath{\nu}}_{f}=2\ensuremathνf​=2 fermionic integer quantum Hall state formed by atoms to a \ensuremathνb=1/2{\ensuremath{\nu}}_{b}=1/2\ensuremathνb​=1/2 bosonic fractional quantum Hall state formed by bosonic diatomic molecules. In the disk geometry we use, these two different topological phases are distinguished by their different gapless edge excitation spectra, and the quantum phase transition between them is signaled by the closing of the energy gap in the bulk. Comparisons will be made with field-theoretical predictions and the case of ppp-wave pairing.
We use exact diagonalization to study the quantum phases and phase transitions when a single species of fermionic atoms at a Landau level filling factor ${\ensuremath{\nu}}_{f}=1$ in a rotating trap interact through a ppp-wave Feshbach resonance. We show that under a weak pairing interaction, the system undergoes a second-order quantum phase transition from a ${\ensuremath{\nu}}_{f}=1$ fermionic integer quantum Hall (FIQH) state at positive detuning, to a ${\ensuremath{\nu}}_{b}=\frac{1}{4}$ bosonic fractional quantum Hall (BFQH) state at negative detuning. However, when the pairing interaction increases, a new phase between them emerges, corresponding to a fraction of fermionic atoms staying in a coherent superposition of a bosonic molecule state and an unbound pair. The phase transition from the FIQH phase to the new phase is of second order and that from the new phase to BFQH phase is of first order.
We consider two-species of fermions in a rotating trap that interact via an s-wave Feshbach resonance, at total Landau level filling factor two (or one for each species). We show that the system undergoes a quantum phase transition from a fermion integer quantum Hall state to a boson fractional quantum Hall state as the pairing interaction strength increases, with the transition occurring near the resonance. The effective field theory for the transition is shown to be that of a (emergent) massless relativistic bosonic field coupled to a Chern-Simons gauge field, with the coupling giving rise to semionic statistics to the emergent particles.
We study a single species of fermionic atoms in an "effective" magnetic field at total filling factor ν(f)=1, interacting through a p-wave Feshbach resonance, and show that the system undergoes a quantum phase transition from a ν(f)=1 fermionic integer quantum Hall state to ν(b)=1/4 bosonic fractional quantum Hall state as a function of detuning. The transition is in the (2+1)D Ising universality class. We formulate a dual theory in terms of quasiparticles interacting with a Z(2) gauge field and show that charge fractionalization follows from this topological quantum phase transition. Experimental consequences and possible tests of our theoretical predictions are discussed.
We numerically study the behavior of spin-1/21/21/2 fermions on a two-dimensional square lattice subject to a uniform magnetic field, where opposite spins interact via an on-site attractive interaction. Starting from the noninteracting case where each spin population is prepared in a quantum Hall state with unity filling, we follow the evolution of the system as the interaction strength is increased. Above a critical value and for sufficiently low flux density, we observe the emergence of a twofold quasidegeneracy accompanied by the opening of an energy gap to the third level. Analysis of the entanglement spectra shows that the gapped ground state is the bosonic 1/21/21/2 Laughlin state. Our work therefore provides compelling evidence of a topological phase transition from the fermionic quantum Hall state at unity filling to the bosonic Laughlin state at a critical attraction strength of the order of the one-body spectrum linewidth.
The parton theory constructs candidate fractional quantum Hall states by decomposing the physical particles into unphysical partons, placing the partons in integer quantum Hall states, and then gluing the partons back into the physical particles. Field theoretical formulations execute the gluing process through the device of emergent gauge fields. Here we study numerically the process of going from the integer quantum Hall effect of two species of fermionic partons to the fractional quantum Hall effect of bosons by introducing an attractive interaction between the fermions of different species and continuously increasing its strength to glue them into bosons. To properly capture the physics in the bulk, we implement this process in a lattice version of the spherical geometry, which allows us to keep the full Hilbert space. Even though the two end-point states are topologically distinct, we find that, for the small system sizes accessible to our study, the energy gap remains open, indicating a crossover between these two states.
The recent production of synthetic magnetic fields acting on electroneutral particles, such as atoms or photons, has boosted interest in the quantum Hall physics of bosons. Adding pseudospin 1/2 to the bosons greatly enriches the scenario, as it allows them to form an interacting integer quantum Hall (IQH) phase with no fermionic counterpart. Here we show that, for a small two-component Bose gas on a disk, the complete strongly correlated regime, extending from the integer phase at filling factor $\ensuremath{\nu}=2$ to the Halperin phase at filling factor $\ensuremath{\nu}=2/3$, is well described by composite fermionization of the bosons. Moreover we study the edge excitations of the IQH state, which, in agreement with expectations from topological field theory, are found to consist of forward-moving charge excitations and backward-moving spin excitations. Finally, we demonstrate how pair-correlation functions allow one to experimentally distinguish the IQH state from competing states, such as non-Abelian spin singlet (NASS) states.