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Crossover from Wannier-Stark localization to charge density waves for interacting spinless fermions in one dimension
Nair Sophia Aucar Boidi1,2, Amnon Aharony3, Ora Entin-Wohlman3
1The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, I-34151 Trieste, Italy.
Journal of Physics. Condensed Matter : an Institute of Physics Journal
|September 12, 2025
Summary
Spinless fermions in an electric field show localized states. Stronger repulsion and weaker fields increase edge region width, potentially forming charge density waves.
Area of Science:
- Condensed Matter Physics
- Quantum Mechanics
- Statistical Mechanics
Background:
- Fermions on finite chains exhibit localization phenomena under external potentials.
- Nearest-neighbor repulsion and electric fields significantly influence particle distribution and energy states.
Purpose of the Study:
- Investigate the behavior of spinless fermions on a finite chain with both nearest-neighbor repulsion and a Wannier-Stark (WS) electric field.
- Analyze the impact of interaction strength and electric field on localization length, ground state occupation, and energy spectrum.
Main Methods:
- Analytical derivation of expressions for localization length.
- Numerical simulations using the density matrix renormalization group (DMRG) technique.
- Calculation of local density of states.
Main Results:
- Localization length is inversely proportional to the electric field strength.
- Ground state occupation decreases from 1 in the bulk to 0 at the edge.
- Edge region width increases with repulsion strength and decreases with electric field strength.
- Charge density waves emerge in the edge region for strong interactions.
- Energy spectrum shows an increasing energy-localized structure (WS ladder) for non-interacting and weakly interacting cases.
Conclusions:
- The study provides analytical and numerical insights into fermion behavior under combined electric fields and interactions.
- Predictions regarding localization length, edge region properties, and spectral features can be experimentally verified using cold atom chains.
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