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Quantum condensed matter in 2D and 3D harbors numerous rich and exotic properties ranging from topological matter with fractional quantum numbers to delicate localization properties and unconventional superconductivity. Unfortunately, much of this physics is beyond analytical or numerical control. In contrast, 1D systems are amenable to special techniques such as the density matrix renormalization group (DMRG), recursive Green's function algorithm, and analytical mappings between spins, fermions, and bosons. Besides uncovering interesting 1D physics, these approaches can provide useful insight into higher dimensional phases, too. Thus, we use various numerical and analytical techniques to investigate strongly correlated states of matter in 1D.
Superconducting diode effects in semimetals
We explore the potential of Weyl and Dirac semimetals as platforms for superconducting diodes -- superconducting counterparts of the famous semiconductor diodes. We find that tilting and band-bending, which are quite common in such semimetals, open up more channels for superconducting pairing and lead to better diode performance.
Schematic of 1D semimetal with tilted and bent bands, which leads to multiple pairing channels.
Multiple pairing channels produce better diode performance in certain regions (red) of parameter space.
When a band asymmetric metal (BAM) is deposited on a conventional superconductor, a current flows at equilibrium and leads to a perfect superconducting diode effect.
Topological defects in band asymmetry with non-zero divergence act as sources/sinks of charge
Exotic superconductivity, perfect superconducting diodes
We investigate 1D metals with skewed bands in proximity to a conventional superconductor. We show that such a metal exhibits a slew of striking behaviors such as an equilibrium supercurrent naively forbidden by fundamental theorems of quantum mechanics, a superconducting diode effect that acquires its theoretical maximum value without fine-tuning, and topological defects that act as sources and sinks of charge. Learn even more
Band asymmetry suppresses localization tendencies
Electrons in 1D metals tend to localize for the slightest impurities, turning the metal insulating. We show a sharp reduction in localization tendencies if the Fermi velocities of left and right movers are unequal. For weak disorder, relevant to the quantum effect of weak localization, a new regime appears where the effect is governed by the velocity mismatch. Localization occurs at strong disorder; however, counterintuitively, finite-size effects appear smaller despite an enhanced localization length. Learn even more
Dispersion of a 1D band asymmetric metal. Note, the left and right Fermi velocities differ in magnitude. θ parameterizes the difference in the next figure.
Localization length (color) increases by 1-2 orders of magnitude for small θ for all disorder strengths (η).
The topological Luttinger liquid (red) has a smooth entanglement entropy profile whereas an ordinary Luttinger liquid (green) has clear oscillations that can be traced to its Fermi wavevector.
Entanglement signatures of topological Luttinger liquids
Topological phases typically have a gapped energy spectrum that protects the topology and have unique entanglement properties that distinguish them from other phases. A recent breakthrough proposed "intrinsically gapless topological phases" as phases that turn topological only when the bulk gap closes. We show that such phases in 1D -- dubbed topological Luttinger liquids (TLLs) -- are characterized by an entanglement entropy profile that lacks Friedel oscillations, unlike ordinary Luttinger liquids. Although TLLs also possess a unique but intricate and non-local string order, our entanglement signature is unbiased and should help detect a TLL even when its string order is unknown. Learn even more
Decoding magic-angle graphene with a 1D model
The ground states of twisted bilayer graphene at the "magic angle" twist of ~1 degree is a critical problem in condensed matter, but theoretical answers face a basic hurdle: the kinetic energy is suppressed, which effectively amplifies the interactions, and our numerical capabilities for strongly interacting systems in 2D are rather limited. In this work, we design a 1D ladder model that shows key parallels with magic-angle graphene. Importantly, interacting 1D systems are perfectly suited for the density matrix renormalization group, which we deploy to reveal a correlated ferromagnet at half-filling, reminiscent of proposals for magic-angle graphene. Learn even more
On the ladder, intra-chain hopping 't', spatially-varying inter-chain hopping 'gamma' and flux 'phi' collude to produce flat bands à la magic-angle graphene. Interactions then give rise to rich, correlated phases calculable by DMRG.
When spins ordered along XYZXYZ..., as shown above, melt but their scalar chirality survives, the result is a phase that breaks time-reversal symmetry but is non-magnetic.
T-symmetry breaking minus magnetism
Usually, time-reversal symmetry-breaking is considered synonymous with magnetism. We propose a state that breaks time-reversal via a scalar chirality of 3 spins along a line, but spin-rotation symmetry stays unbroken due to the Mermin-Wagner theorem. Using the density matrix renormalization group, we show that the phase indeed occurs in a spin-1 chain with exchange and quartic interactions. Surprisingly, this phase could be at play in the pseudogap phase of the underdoped cuprates, where polar Kerr effect experiments indicate broken time-reversal symmetry, but NMR has not found magnetism. Learn even more about the original proposal and the proof in 1D
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