We obtain the phase diagram of a Bose-Fermi mixture of hardcore spinless bosons and spin-polarized fermions with nearest-neighbor intraspecies interaction and on-site interspecies repulsion in an optical lattice at half filling using a slave-boson mean-field theory. We show that such a system can have four possible phases which are (a) supersolid bosons coexisting with fermions in the Mott state, (b) Mott state of bosons coexisting with fermions in a metallic or charge-density wave state, (c) a metallic fermionic state coexisting with superfluid phase of bosons, and (d) Mott insulating state of fermions and bosons. We chart out the phase diagram of the system and provide analytical expressions for the phase boundaries within mean-field theory. We demonstrate that the transitions between these phases are generically first order with the exception of that between the supersolid and the Mott states which, within mean-field theory, is a continuous quantum phase transition. We also obtain the low-energy collective excitations of the system in these phases. Finally, we study the particle-hole excitations in the Mott insulating phase and use it to determine the dynamical critical exponent $z$ for the supersolid-Mott insulator transition. We discuss experiments which can test our theory.We obtain the phase diagram of a Bose-Fermi mixture of hardcore spinless bosons and spin-polarized fermions with nearest-neighbor intraspecies interaction and on-site interspecies repulsion in an optical lattice at half filling using a slave-boson mean-field theory. We show that such a system can have four possible phases which are (a) supersolid bosons coexisting with fermions in the Mott state, (b) Mott state of bosons coexisting with fermions in a metallic or charge-density wave state, (c) a metallic fermionic state coexisting with superfluid phase of bosons, and (d) Mott insulating state of fermions and bosons. We chart out the phase diagram of the system and provide analytical expressions for the phase boundaries within mean-field theory. We demonstrate that the transitions between these phases are generically first order with the exception of that between the supersolid and the Mott states which, within mean-field theory, is a continuous quantum phase transition. We also obtain the low-energy collective excitations of the system in these phases. Finally, we study the particle-hole excitations in the Mott insulating phase and use it to determine the dynamical critical exponent $z$ for the supersolid-Mott insulator transition. We discuss experiments which can test our theory.

arXiv:0811.4515Physical Review BMar 24, 200916 citations

Fermionic spin liquid analysis of the paramagnetic state in volborthite

Li Ern Chern, Robert Schaffer, Sopheak Sorn +1 more

Recently, thermal Hall effect has been observed in the paramagnetic state of volborthite, which consists of distorted kagome layers with $S=1/2$ local moments. Despite the appearance of magnetic order below $1\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ , the response to external magnetic field and unusual properties of the paramagnetic state above $1\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ suggest possible realization of exotic quantum phases. Motivated by these discoveries, we investigate possible spin liquid phases with fermionic spinon excitations in a nonsymmorphic version of the kagome lattice, which belongs to the two-dimensional crystallographic group $p2gg$ . This nonsymmorphic structure is consistent with the spin model obtained in the density functional theory calculation. Using projective symmetry group analysis and fermionic parton mean field theory, we identify twelve distinct ${\mathbb{Z}}_{2}$ spin liquid states, four of which are found to have correspondence in the eight Schwinger boson spin liquid states we classified earlier. We focus on the four fermionic states with bosonic counterpart and find that the spectrum of their corresponding root $U(1)$ states features spinon Fermi surface. The existence of spinon Fermi surface in candidate spin liquid states may offer a possible explanation of the finite thermal Hall conductivity observed in volborthite.Recently, thermal Hall effect has been observed in the paramagnetic state of volborthite, which consists of distorted kagome layers with $S=1/2$ local moments. Despite the appearance of magnetic order below $1\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, the response to external magnetic field and unusual properties of the paramagnetic state above $1\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ suggest possible realization of exotic quantum phases. Motivated by these discoveries, we investigate possible spin liquid phases with fermionic spinon excitations in a nonsymmorphic version of the kagome lattice, which belongs to the two-dimensional crystallographic group $p2gg$. This nonsymmorphic structure is consistent with the spin model obtained in the density functional theory calculation. Using projective symmetry group analysis and fermionic parton mean field theory, we identify twelve distinct ${\mathbb{Z}}_{2}$ spin liquid states, four of which are found to have correspondence in the eight Schwinger boson spin liquid states we classified earlier. We focus on the four fermionic states with bosonic counterpart and find that the spectrum of their corresponding root $U(1)$ states features spinon Fermi surface. The existence of spinon Fermi surface in candidate spin liquid states may offer a possible explanation of the finite thermal Hall conductivity observed in volborthite.

arXiv:1703.09220Physical review. B./Physical review. BOct 10, 201710 citations

Quantum mechanics and quantum field theory of a fermion system

Wolfgang Bulla, K. Unterkofler

Jan 1, 19860 citations

Coherent states for bosons and fermions

Luca Salasnich

Springer eBooksJan 1, 20201 citation

z

for the supersolid-Mott insulator transition. We discuss experiments which can test our theory.

Recently, thermal Hall effect has been observed in the paramagnetic state of volborthite, which consists of distorted kagome layers with

S=1/2

local moments. Despite the appearance of magnetic order below

1\phantom{\rule{0.28em}{0ex}}\mathrm{K}

, the response to external magnetic field and unusual properties of the paramagnetic state above

1\phantom{\rule{0.28em}{0ex}}\mathrm{K}

suggest possible realization of exotic quantum phases. Motivated by these discoveries, we investigate possible spin liquid phases with fermionic spinon excitations in a nonsymmorphic version of the kagome lattice, which belongs to the two-dimensional crystallographic group

p2gg

. This nonsymmorphic structure is consistent with the spin model obtained in the density functional theory calculation. Using projective symmetry group analysis and fermionic parton mean field theory, we identify twelve distinct

{\mathbb{Z}}_{2}

spin liquid states, four of which are found to have correspondence in the eight Schwinger boson spin liquid states we classified earlier. We focus on the four fermionic states with bosonic counterpart and find that the spectrum of their corresponding root

U(1)

states features spinon Fermi surface. The existence of spinon Fermi surface in candidate spin liquid states may offer a possible explanation of the finite thermal Hall conductivity observed in volborthite.