2D Fermions Research Articles

A modular implementation of an effective interaction approach for harmonically trapped fermions in 1D

We introduce a generic and accessible implementation of an exact diagonalization method for studying few-fermion models. Our aim is to provide a testbed for the newcomers to the field as well as a stepping stone for trying out novel optimizations and approximations. This userguide consists of a description of the algorithm, and several examples in varying orders of sophistication. In particular, we exemplify our routine using an effective-interaction approach that fixes the low-energy physics. We benchmark this approach against the existing data, and show that it is able to deliver state-of-the-art numerical results at a significantly reduced computational cost.

Spacetime duality between localization transitions and measurement-induced transitions

Time evolution of quantum many-body systems typically leads to a state with maximal entanglement allowed by symmetries. Two distinct routes to impede entanglement growth are inducing localization via spatial disorder, or subjecting the system to non-unitary evolution, e.g., via projective measurements. Here we employ the idea of space-time rotation of a circuit to explore the relation between systems that fall into these two classes. In particular, by space-time rotating unitary Floquet circuits that display a localization transition, we construct non-unitary circuits that display a rich variety of entanglement scaling and phase transitions. One outcome of our approach is a non-unitary circuit for free fermions in 1d that exhibits an entanglement transition from logarithmic scaling to volume-law scaling. This transition is accompanied by a 'purification transition' analogous to that seen in hybrid projective-unitary circuits. We follow a similar strategy to construct a non-unitary 2d Clifford circuit that shows a transition from area to volume-law entanglement scaling. Similarly, we space-time rotate a 1d spin chain that hosts many-body localization to obtain a non-unitary circuit that exhibits an entanglement transition. Finally, we introduce an unconventional correlator and argue that if a unitary circuit hosts a many-body localization transition, then the correlator is expected to be singular in its non-unitary counterpart as well.

Free fermion entanglement with a semitransparent interface: the effect of graybody factors on entanglement islands

We study the entanglement entropy of free fermions in 2d in the presence of a partially transmitting interface that splits Minkowski space into two half-spaces. We focus on the case of a single interval that straddles the defect, and compute its entanglement entropy in three limits: Perturbing away from the fully transmitting and fully reflecting cases, and perturbing in the amount of asymmetry of the interval about the defect. Using these results within the setup of the Poincaré patch of AdS_22 statically coupled to a zero temperature flat space bath, we calculate the effect of a partially transmitting AdS_22 boundary on the location of the entanglement island region. The partially transmitting boundary is a toy model for black hole graybody factors. Our results indicate that the entanglement island region behaves in a monotonic fashion as a function of the transmission/reflection coefficient at the interface.

Correlated nature of hybrid s -wave superconducting and Rashba lattices

We elucidate the electronic state of a two-dimensional (2D) Rashba square lattice proximitized to a square monolayer $s$-wave superconductor, analyzing the role played by dynamical electron-electron interactions. The $\text{2D}+\text{2D}$ proximity effect induces sharp Bogoliubov and low-energy Andreev-reflected bound states, suppressing the $s$-wave gap globally. Dynamical correlations strongly renormalize the Bogoliubov quasiparticles and the Andreev levels, evolving the spin-resolved Andreev linewidths into a single bound state. We explore the channel- and spin-resolved spectral functions and analyze the reconstructed superconducting state, showing that the Rashba spin-orbit coupling drives strong channel differentiation. The mutual interplay between electron-electron and spin-orbit interactions, with proximity-induced electron pairing, lead us to introduce a generally applicable mechanism for designing Majorana fermions in 2D superconducting structures.

Thermodynamics and static response of anomalous one-dimensional fermions via a quantum Monte Carlo approach in the worldline representation

A system of three-species fermions in one spatial dimension (1D) with a contact three-body interaction is known to display a scale anomaly. This anomaly is identical to that of a two-dimensional (2D) system of two-species fermions. The exact relation between those two systems, however, is limited to the two-particle sector of the 2D case and the three-particle sector of the 1D case. Here, we implement a non-perturbative Monte Carlo approach, based on the worldline representation, to calculate the thermodynamics and static response of three-species fermions in 1D, thus tackling the many-body sector of the problem. We determine the energy, density, and pressure equations of state, and the compressibility and magnetic susceptibility for a wide range of temperatures and coupling strengths. We compare our results with the third-order virial expansion.

Effective magnetic field induced by inhomogeneous Fermi velocity in strained honeycomb structures

In addition to the known pseudomagnetic field, nonuniform strains independently induce a position-dependent Fermi velocity (PDFV) in graphene. Here we demonstrate that, due to the presence of a PDFV, the Dirac fermions on a nonuniform (strained) honeycomb lattice may experiment a sort of magnetic effect, which is linearly proportional to the momentum of the quasiparticle. As a consequence, the quasiparticles have a sublinear dispersion relation. Moreover, we analyze the general consequence of a PDFV on the Klein tunneling of electrons through pseudomagnetic barriers. In particular, we report an anomalous (Klein) tunneling for an electron passing across velocity barriers with magnetic features. Our findings about the effects induced by a PDFV on Dirac fermions in (2D) strained honeycomb lattice could be extended to (3D) Dirac and Weyl semimetals and/or its analogous artificial systems.

Fermi–Bose mixture in mixed dimensions

One of the challenging goals in the studies of many-body physics with ultracold atoms is the creation of a topological superfluid for identical fermions in two dimensions (2D). The expectations of reaching the critical temperature Tc through p-wave Feshbach resonance in spin-polarized fermionic gases have soon faded away because on approaching the resonance, the system becomes unstable due to inelastic-collision processes. Here, we consider an alternative scenario in which a single-component degenerate gas of fermions in 2D is paired via phonon-mediated interactions provided by a 3D BEC background. Within the weak-coupling regime, we calculate the critical temperature Tc for the fermionic pair formation using the Bethe–Salpeter formalism, and show that it is significantly boosted by higher-order diagrammatic terms, such as phonon dressing and vertex corrections. We describe in detail an experimental scheme to implement our proposal, and show that the long-sought p-wave superfluid is at reach with state-of-the-art experiments.

On the new Continuous Matrix Product Ansatz

The fertile new field of quantum information theory is inspiring new ways to study correlated quantum systems by providing fresh insights into the structure of their Hilbert spaces. One of the latest developments in this direction was the extension of the ubiquitous matrix-product-state constructions, epitomized by the density-matrix renormalization-group algorithm, to continuous space-time; so as to be able to describe low-dimensional field theories within a variational approach. Following the earlier success achieved for bosonic theories, we present the first implementation of a continuous matrix product state (cMPS) for spinfull non-relativistic fermions in 1D. We propose a construction of variational matrices with an efficient parametrization that respects the translational symmetry of the problem (without being overly constraining) and readily meets the regularity conditions that arise from removing the ultraviolet divergences in the kinetic energy. We tested the validity of our approach on an interacting spin-1/2 system with spin imbalance. We observe that the ansatz correctly predicts the ground-state magnetic properties for the attractive spin-1/2 Fermi gas, including a phase-oscillating pair correlation function in the partially polarized regime (the 1D correlate of the FFLO state). We shall also discuss how to generalize the cMPS ansatz to other situations.

Berezinskii-Kosterlitz-Thouless phase transition in 2D spin-orbit-coupled Fulde-Ferrell superfluids.

The experimental observation of traditional Zeeman-field induced Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids has been hindered by various challenges, in particular, the requirement of low dimensional systems. In 2D, finite temperature phase fluctuations lead to an extremely small Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for FFLO superfluids, raising serious concerns regarding their experimental observability. Recently, it was shown that FFLO superfluids can be realized using a Rashba spin-orbit coupled Fermi gas subject to Zeeman fields, which may also support topological excitations such as Majorana fermions in 2D. Here we address the finite temperature BKT transition issue in this system, which may exhibit gapped, gapless, topological, and gapless topological FF phases. We find a large BKT transition temperature due to large effective superfluid densities, making it possible to observe 2D FF superfluids at finite temperature. In addition, we show that gapless FF superfluids can be stable due to their positive superfluid densities. These findings pave the way for the experimental observation of 2D gapped and gapless FF superfluids and their associated topological excitations at finite temperature.

Finding Density Functionals with Machine Learning

Machine learning is used to approximate density functionals. For the model problem of the kinetic energy of noninteracting fermions in 1D, mean absolute errors below 1 kcal/mol on test densities similar to the training set are reached with fewer than 100 training densities. A predictor identifies if a test density is within the interpolation region. Via principal component analysis, a projected functional derivative finds highly accurate self-consistent densities. The challenges for application of our method to real electronic structure problems are discussed.

Fluctuation Spectral Functions and Phase Transitions for Cold Fermi Gases in 2D

We study cold fermions in 2D that are interacting through the s-wave contact potential, using the path-integral formalism. The phase transitions are investigated using the joint solution of the gap and number equations. In the latter ones, the amplitude and phase fluctuations are taken into account within the t-matrix NSR-type formalism. It is shown that convergent solutions for the fermion density in 2D can be obtained even in the lowest-order (quadratic) approximation for fluctuations with a proper determination of the spectral functions. This approach leads, in particular, to a non-coherent quasicondensate which exists between the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature below which the system is superfluid and a transition temperature TΔ above which the quasicondensate is destroyed.

Partially Gapped Fermions in 2D

We compute mean field phase diagrams of two closely related interacting fermion models in two spatial dimensions (2D). The first is the so-called 2D t-t'-V model describing spinless fermions on a square lattice with local hopping and density-density interactions. The second is the so-called 2D Luttinger model that provides an effective description of the 2D t-t'-V model and in which parts of the fermion degrees of freedom are treated exactly by bosonization. In mean field theory, both models have a charge-density-wave (CDW) instability making them gapped at half-filling. The 2D t-t'-V model has a significant parameter regime away from half-filling where neither the CDW nor the normal state are thermodynamically stable. We show that the 2D Luttinger model allows to obtain more detailed information about this mixed region. In particular, we find in the 2D Luttinger model a partially gapped phase that, as we argue, can be described by an exactly solvable model.

Towards a simulation of disordered systems with interactions

We consider the problem of Anderson localization in disordered systems with interactions.We present a numerical approach in quasi-one-dimensional (quasi-1D) systemswhich combines aspects of the transfer matrix and Green’s function recursionmethods with the density matrix renormalization group. The method is applied tospinless fermions in 1D and a generalization to finite cross-sections is outlined.

Localization in disordered systems with interactions

We present an improved numerical approach to the study of disorder and interactions in quasi-1D systems which combines aspects of the transfer matrix method and the density matrix renormalization group which have been successfully applied to disorder and interacting problems respectively. The method is applied to spinless fermions in 1D and a generalization to finite cross-sections is outlined.

Interaction effects on two-dimensional fermions with random hopping

We study the effects of generic short-ranged interactions on a system of 2D Dirac fermions subject to a special kind of static disorder, often referred to as ``chiral.'' The non-interacting system is a member of the disorder class BDI [M. R. Zirnbauer, J. Math. Phys. 37, 4986 (1996)]. It emerges, for example, as a low-energy description of a time-reversal invariant tight-binding model of spinless fermions on a honeycomb lattice, subject to random hopping, and possessing particle-hole symmetry. It is known that, in the absence of interactions, this disordered system is special in that it does not localize in 2D, but possesses extended states and a finite conductivity at zero energy, as well as a strongly divergent low-energy density of states. In the context of the hopping model, the short-range interactions that we consider are particle-hole symmetric density-density interactions. Using a perturbative one-loop renormalization group analysis, we show that the same mechanism responsible for the divergence of the density of states in the non-interacting system leads to an instability, in which the interactions are driven strongly relevant by the disorder. This result should be contrasted with the limit of clean Dirac fermions in 2D, which is stable against the inclusion of weak short-ranged interactions. Our work suggests a novel mechanism wherein a clean system, initially insensitive to interaction effects, can be made unstable to interactions upon the inclusion of weak static disorder.

Ferromagnetic nanoclusters in two-dimensionalHe3

$^{3}\mathrm{He}$ adsorbed on graphite is an almost ideal two-dimensional (2D) fermionic system. The 2D solid, where the interaction between the nuclear spins $S=\frac{1}{2}$ is due to multiple spin exchange, has been extensively studied as a model system for strongly interacting fermions in 2D. At high densities in the second layer, three-body exchange dominates and leads to Heisenberg ferromagnetism. We report on nuclear magnetic resonance measurements at ultralow temperatures and low magnetic fields of the second layer of $^{3}\mathrm{He}$ on graphite preplated by one layer of $^{4}\mathrm{He}$. By adding controlled amounts of $^{4}\mathrm{He}$, $^{3}\mathrm{He}$ atoms are pushed out from the ferromagnetic domains, which become smaller and denser. We can evaluate the properties of these clusters, and control their size from a few tens to a few hundreds of atoms. These sizes are comparable to today's computing capabilities for exact numerical calculations on small clusters, and should lead to direct comparison between measurements on this model Heisenberg system and theory.

Classical field theory of transport of interacting classical particles through one-dimensional channels

A classical field theory is constructed to describe the interacting classical particles in one-dimensional (1D) channels. We show the intrinsic connection between the classical field theory and the corresponding quantum theory, i.e., Tomonaga-Luttinger liquid theory, which describes the interacting fermions in 1D. As applications, we calculate the particle density function along the tube axis and the particle current through the channels by explicitly including the particle-particle and particle-wall interactions and we find quantum-classical correspondence in the conductance formula.

Disorder and interactions in one-dimensional systems

We present a new numerical approach to the study of disorder and interactions in quasi-1D systems which combines aspects of the transfer matrix method and the density matrix renormalization group which have been successfully applied to disorder and interacting problems respectively. The method is applied to spinless fermions in 1D and the existence of a conducting state is demonstrated in the presence of attractive interactions.

Luttinger liquid versus charge density wave behaviour in the one-dimensional spinless fermion Holstein model

We discuss the nature of the different ground states of the half-filled Holstein model of spinless fermions in 1D. In the metallic regime we determine the renormalised effective coupling constant and the velocity of the charge excitations by a density-matrix renormalisation group (DMRG) finite-size scaling approach. At low (high) phonon frequencies the Luttinger liquid is characterised by an attractive (repulsive) effective interaction. In the charge-density wave Peierls-distorted state the charge structure factor scales to a finite value indicating long-range order.

Large-Ntheory of strongly commensurate dirty bosons: absence of a transition in two dimensions

The spherical limit of strongly commensurate dirty-bosons is studied perturbatively at weak disorder and numerically at strong disorder in two dimensions (2D). We argue that disorder is not perfectly screened by interactions, and consequently that the ground state in the effective Anderson localisation problem always remains localised. As a result there is only a gapped Mott insulator phase in the theory. Comparisons with other studies and the parallel with disordered fermions in 2D are discussed. We conjecture that while for the physical cases N=2 (XY) and N=1 (Ising) the theory should have the ordered phase, it may not for N=3 (Heisenberg).