Interplay of quantum phase transition and flat band in hybrid lattices

We investigate the interplay of superradiant phase transition (SPT) and energy band physics in an extended Dicke-Hubbard lattice whose unit cell consists of a Dicke model coupled to an atomless cavity. We found in such a periodic lattice the critical point that occurs in a single Dicke model becomes a critical region that is periodically changing with the wavenumber $k$ . In the weak-coupling normal phase of the system we observed a flat band and its corresponding localization that can be controlled by the ground-state SPT. Our work builds the connection between flat band physics and SPT, which may fundamentally broaden the regimes of many-body theory and quantum optics.We investigate the interplay of superradiant phase transition (SPT) and energy band physics in an extended Dicke-Hubbard lattice whose unit cell consists of a Dicke model coupled to an atomless cavity. We found in such a periodic lattice the critical point that occurs in a single Dicke model becomes a critical region that is periodically changing with the wavenumber $k$. In the weak-coupling normal phase of the system we observed a flat band and its corresponding localization that can be controlled by the ground-state SPT. Our work builds the connection between flat band physics and SPT, which may fundamentally broaden the regimes of many-body theory and quantum optics.

Oct 2, 20191 citation

Disorder and robustness of superconductivity on the quasi-one-dimensional flat-band Creutz lattice

Si Min Chan, Benoît Grémaud, G. G. Batrouni

We study the interplay between on-site disorder and fermion pairing on the quasi-one-dimensional flat-band Creutz lattice. Both disorder and flat bands localize particles, but an attractive interaction results in pair formation and delocalization giving rise to superconductivity. In this work, we examine the attractive Hubbard model on the Creutz lattice to study the competition between these two effects and elucidate the properties of the superconducting phase and the localization quantum phase transition as the disorder strength is increased. Our main result is that flat-band superconductivity is robust against disorder: The critical disorder strength ${W}_{c}$ required to localize the fermion pairs and destroy superconductivity is finite at any interaction strength $U$ and is proportional to the superconducting weight ${D}_{s}$ of the clean system. Using large-scale density matrix renormalization group computations, we show that this transition is of the Berezinskii-Kosterlitz-Thouless form. In addition, even at very small interaction strength, the localization is not due to single-fermion localization but to pair localization. For completeness, we briefly study this disorder-induced localization with mean field theory and show that ${W}_{c}$ can be accurately determined by using an appropriate scaling function.We study the interplay between on-site disorder and fermion pairing on the quasi-one-dimensional flat-band Creutz lattice. Both disorder and flat bands localize particles, but an attractive interaction results in pair formation and delocalization giving rise to superconductivity. In this work, we examine the attractive Hubbard model on the Creutz lattice to study the competition between these two effects and elucidate the properties of the superconducting phase and the localization quantum phase transition as the disorder strength is increased. Our main result is that flat-band superconductivity is robust against disorder: The critical disorder strength ${W}_{c}$ required to localize the fermion pairs and destroy superconductivity is finite at any interaction strength $U$ and is proportional to the superconducting weight ${D}_{s}$ of the clean system. Using large-scale density matrix renormalization group computations, we show that this transition is of the Berezinskii-Kosterlitz-Thouless form. In addition, even at very small interaction strength, the localization is not due to single-fermion localization but to pair localization. For completeness, we briefly study this disorder-induced localization with mean field theory and show that ${W}_{c}$ can be accurately determined by using an appropriate scaling function.

arXiv:2506.07095Physical review. B./Physical review. BAug 19, 20252 citations

Quantum Phase transitions in Hubbard lattices

Matteo Rizzi, Rosario Fazio

Jan 1, 20071 citation

Characterizing the Quantum Phase Transition using a Flat Band in Circuit QED Lattices

Gui‐Lei Zhu, Xin-You Lü, Hamidreza Ramezani

We show the superradiant phase transition (SPT) can control the existence of flat band in an extended Dicke-Hubbard lattice [1].

Conference on Lasers and Electro-OpticsJan 1, 20200 citations

Phase Transitions in Quantum Systems

WORLD SCIENTIFIC eBooksNov 1, 20130 citations

k

. In the weak-coupling normal phase of the system we observed a flat band and its corresponding localization that can be controlled by the ground-state SPT. Our work builds the connection between flat band physics and SPT, which may fundamentally broaden the regimes of many-body theory and quantum optics.

{W}_{c}

required to localize the fermion pairs and destroy superconductivity is finite at any interaction strength

U

and is proportional to the superconducting weight

{D}_{s}

of the clean system. Using large-scale density matrix renormalization group computations, we show that this transition is of the Berezinskii-Kosterlitz-Thouless form. In addition, even at very small interaction strength, the localization is not due to single-fermion localization but to pair localization. For completeness, we briefly study this disorder-induced localization with mean field theory and show that

{W}_{c}

can be accurately determined by using an appropriate scaling function.