Metric-Space Approach for Distinguishing Quantum Phase Transitions in Spin-Imbalanced Systems

Abstract

Metric spaces are characterized by distances between pairs of elements. Systems that are physically similar are expected to present smaller distances (between their densities, wave functions and potentials) than systems that present different physical behaviors. For this reason metric spaces are good candidates for probing quantum phase transitions, since they could identify regimes of distinct phases. Here we apply metric space analysis to explore the transitions between the several phases in spin imbalanced systems. In particular we investigate the so-called FFLO (Fulde-Ferrel-Larkin-Ovchinnikov) phase, which is an intriguing phenomenon in which superconductivity and magnetism coexist in the same material. This is expected to appear for example in attractive fermionic systems with spin-imbalanced populations, due to the internal polarization produced by the imbalance. The transition between FFLO phase (superconducting phase) and the normal phase (non-superconducting) and their boundaries have been subject of discussion in recent years. We consider the Hubbard model in the attractive regime for which Density Matrix Renormalization Group calculations allow us to obtain the exact density function of the system. We then analyze the exact density distances as a function of the polarization. We find that our distances display signatures of the distinct quantum phases in spin-imbalanced fermionic systems: with respect to a central reference polarization, systems without FFLO present a very symmetric behavior, while systems with phase transitions are asymmetric.

Many-body effects on the thermodynamics of closed quantum systems

“…The one-dimensional Hubbard model can depict systems from weakly to strongly correlated and model numerous phases of matter and related phase transitions, such as metallic, antiferromagnetic, Mott-insulator, superconductivity, and FFLO transition [18][19][20][21]. It is being widely used to study many physical systems, from coupled quantum dots, to molecules, to chains of atoms [22][23][24][25][26][27].…”

Approximating quantum thermodynamic properties using DFT

“…It is used to simulate structures such as chains of atoms or coupled quantum dots [29][30][31][32][33][34], which are relevant as hardware for quantum technologies. It also allows representation of a wide range of phases of matter: metallic, Mottinsulating, band-insulating [35], and even superconducting [26,[36][37][38][39][40][41].…”

Simulating Artificial 1D Physics with Ultra‐Cold Fermionic Atoms: Three Exemplary Themes

“…For this reason, the unconventional FFLO pairing in ultra‐cold 1D systems has recently been deeply investigated theoretically from various perspectives, for both confined [ 54–57 ] and lattice systems. [ 58–62 ] Quasi‐1D quantum simulators created with ultra‐cold neutral atoms constitute a highly controllable environment, where the Fermi surface mismatch can be precisely tuned by changing the spin composition of the initial population, rather than with external magnetic fields. [ 63–67 ] The relative spin populations can be tuned, for example, by driving radio‐frequency sweeps between the states at different powers.…”