arXiv subjects

Adrian Kantian

Publications and source records attributed to Adrian Kantian.

At least 19 recordsLinked to original sources

arXiv2026

Predicting critical temperature in quantum simulators for high-$T_c$ superconductivity: the matrix product state plus mean field approach

Quantum simulation based on ultra cold atomic lattice gases is one of the most promising platforms to investigate high-$T_c$ superconductivity beyond the limited capabilities of quantum many body numerics on classical computers. Yet, despite enormous progress since the field's inception, realizing a high-$T_c$ superconducting state still remains out of reach. The present work lays the groundwork to purpose the recently proposed, and already partly realized, mixed-dimensional (mixD) models, towards this end. These systems offer the proven capability to realize very high pairing energies while retaining appreciable mobility of pairs. We specifically investigate the potential of 2D mixD-models with anisotropic tunneling, using the matrix product state plus mean field theory (MPS+MF) for fermions, and show that these models may enter a high-$T_c$ superconducting phase. These simulations in turn are based on a comprehensive characterization of the 1D mixD-systems, which are the sub-units of which the 2D system is comprized. In this, we cover the range of currently experimentally relevant system sizes, and establish practical heuristics to determine when finite\hyp size effects preclude the use of a 1D mixD-system to build the 2D ones.

cond-mat.supr-con↗

arXiv2026

Enhancement of superconducting stiffness in hybrid superconducting-metallic bilayers

Boosting superconductivity by metallic reservoirs is the essence of Kivelson's bilayer proposal. One layer provides pairing to the electrons, while the weakly coupled metal provides additional phase coherence to those pairs by mediating extended-range pair-pair coupling. Demonstrating significant and unambiguous performance gains with strong-coupling methods for such set-ups had been difficult. In the present work, we study these systems doped away from half-filling, corresponding to a partially spin-polarized 1D Anderson- or Kondo-lattice. We show that this breaks the coexistence of dominant superconducting and density-density correlations decisively in favour or the former. Consequently, we provide evidence that in this doped regime, superconducting near-long-range order is not precluded by a small charge-gap in the thermodynamic limit, as we have recently shown to be the case at half-filling [JE Ebot $et$ $al.$, arXiv:2602.11153 [cond-mat.supr-con]]. We study the complex manner in which the enhancement of superconductivity in the pairing layer depends on the parameters of the metal, and especially that both pairing-limited and stiffness-limited regimes may appear in these systems. In addition to superconducting bilayers, our results are relevant, via a particle-hole transformation, for heavy-fermion Kondo-lattice materials in magnetic fields, as we provide previously lacking insight on the competition between antiferromagnetic and easy-plane magnetism, as well as a route for comprehensive indirect tests of Kivelson's bilayer proposal well beyond previous capabilities.

cond-mat.supr-con↗

arXiv2026

Mapping reservoir-enhanced superconductivity to near-long-range magnetic order in the undoped one-dimensional Anderson and Kondo lattices

The undoped Kondo necklace in 1D is a paradigmatic and well understood model of a Kondo insulator. This work performs the first large-scale study of the 1D Anderson-lattice underlying the Kondo necklace with quasi-exact numerical methods, comparing this with the perturbative effective 1D Kondo-necklace model derived from the former. This study is based on an exact mapping of the Anderson model to one of a superconducting pairing layer connected to a metallic reservoir which is valid in arbitrary spatial dimensions, thereby linking the previously disparate areas of reservoir-enhanced superconductivity, following Kivelson's pioneering proposals, and that of periodic Kondo-systems. Our work reveals that below the length-scales on which the insulating state sets in, which can be very large, superconducting and density-density correlations are degenerate and may both appear to approach an almost ordered state, to a degree that far exceeds that of any isolated 1D pairing layer with short-range interactions. We trace these effects to the effective extended-range coupling that the metallic layer mediates within the pairing layer. These results translate directly to the appearance of near-long-range magnetic order at intermediate scales in the Kondo-systems, and explain the strong renormalization of the RKKY-coupling that we effectively observe, in terms of the back-action of the pairing layer onto the metallic layer. The effects we predict could be tested either by local probes of quasi-1D heavy fermion compounds such as CeCo$_2$Ga$_8$, in engineered chains of ad-atoms or in ultracold atomic gases.

cond-mat.str-el↗

arXiv2025

Strong enhancements to superconducting properties of 1D systems from metallic reservoirs

Using a 1D bilayer system comprised of pairing and metallic layers, the present work proves the striking power of reservoir-mediated boosting of superconductivity. Employing many-body numerics on large systems at zero and finite temperature, we unravel the complex processes by which the tuning of the metal parameters can impact the effective pairing strength as well as the long-range pair-pair-coupling mediated by the metal. It is these two processes that in turn can strongly enhance superconducting susceptibility and thermal superconducting correlation length over those of the isolated system. We show that in this way, even a 1D system can come very close to achieving superconducting long-range order.

cond-mat.supr-con↗

arXiv2025

Ground states of quasi-two-dimensional correlated systems via energy expansion

We introduce a generic method for computing groundstates that is applicable to a wide range of spatially anisotropic 2D many-body quantum systems. By representing the 2D system using a low-energy 1D basis set, we obtain an effective 1D Hamiltonian that only has quasi-local interactions, at the price of a large local Hilbert space. We apply our new method to three specific 2D systems of weakly coupled chains: hardcore bosons, a spin-$1/2$ Heisenberg Hamiltonian, and spinful fermions with repulsive interactions. In particular, we showcase a non-trivial application of the energy expansion framework, to the anisotropic triangular Heisenberg lattice, a highly challenging model related to 2D spin liquids. Treating lattices of unprecedented size, we provide evidence for the existence of a quasi-1D gapless spin liquid state in this system. We also demonstrate the energy expansion-framework to perform well where external validation is possible. For the fermionic benchmark in particular, we showcase the energy expansion-framework's ability to provide results of comparable quality at a small fraction of the resources required for previous computational efforts.

cond-mat.str-el↗

arXiv2024

Fusing matrix-product states with quantum Monte Carlo: reducing entanglement and sign problem at the same time

Systems of correlated quantum matter can be a steep challenge to any would-be method of solution. Matrix-product state (MPS)-based methods can describe 1D systems quasiexactly, but often struggle to retain sufficient bipartite entanglement to accurately approximate 2D systems already. Conversely, Quantum Monte Carlo (QMC) approaches, based on sampling a probability distribution, can generally approximate 2D and 3D systems with an error that decays systematically with growing sampling size. However, QMC can suffer from the so-called sign problem, that makes the approach prohibitively costly for many systems of interest, such as repulsively interacting fermions away from commensurate densities and frustrated systems. In this article, we introduce a new hybrid approach, that combines auxiliary-field QMC (AFQMC) with MPS-based algorithms. This hybrid technique removes or reduces the sign problem (depending on the specific model) while also needing to retain much lower bipartite entanglement than brute-force application of a MPS-algorithm, without the use of uncontrolled approximations. We present two use-cases of the algorithm that would be challenging or impossible to address with any other approach, and quantify the extent of any remaining sign problem.

cond-mat.str-el↗

arXiv2023

Mobile Impurity in a Two-Leg Bosonic Ladder

We study the dynamics of a mobile impurity in a two-leg bosonic ladder. The impurity moves both along and across the legs and interacts with a bath of interacting bosonic particles present in the ladder. We use both analytical (Tomonaga-Luttinger liquid - TLL) and numerical (Density Matrix Renormalization Group - DMRG) methods to compute the Green's function of the impurity. We find that for a small impurity-bath interaction, the bonding mode of the impurity effectively couples only to the gapless mode of the bath while the anti-bonding mode of the impurity couples to both gapped and gapless mode of the bath. We compute the time dependence of the Green's function of the impurity, for impurity created either in the anti-bonding or bonding mode with a given momentum. The later case leads to a decay as a power-law below a critical momentum and exponential above, while the former case always decays exponentially. We compare the DMRG results with analytical results using the linked cluster expansion and find a good agreement. In addition we use DMRG to extract the lifetime of the quasi-particle, when the Green's function decays exponentially. We also treat the case of an infinite bath-impurity coupling for which both the bonding and antibonding modes are systematically affected. For this case the impurity Green's function in the bonding mode decays as a power-law at zero momentum.The corresponding exponent increases with increasing transverse-tunneling of the impurity. We compare our results with the other impurity problems for which the motion of either the impurity or the bath is limited to a single chain. Finally we comments on the consequences of our findings for experiments with the ultracold gasses.

cond-mat.quant-gas↗

arXiv2023

Resolving competition of charge-density wave and superconducting phases using the MPS+MF algorithm

Materials with strong electronic correlations may exhibit a superconducting (SC) phase when tuning some parameters, but they almost always also have multiple other phases, typically insulating ones, that are in close competition with SC. It is highly challenging to resolve this competition with quantitative numerics for the group of quasi-two-dimensional materials such as the cuprates. This is the case even for the simplified minimal models of these materials, the doped 2D Hubbard model with repulsive interactions, where clusters of sufficient size to determine the phase in the thermodynamic limit can be hard-to-impossible to treat in practice. The present work shows how quasi-one-dimensional systems, 2D and 3D arrays of weakly coupled 1D correlated electrons, are much more amenable to resolve the competition between SC and insulating orders on an equal footing using matrix-product states (MPS). Using the recently established MPS plus mean field (MPS+MF) approach for fermions, we demonstrate that large systems are readily reachable in these systems, and thus the thermodynamic regime by extrapolation. Focusing on basic model systems, 3D arrays of negative-U Hubbard chains with additional nearest-neighbor interaction V, we show that despite the MF component of the MPS+MF technique we can reproduce the expected coexistence of SC and charge-density wave at V=0 for density n=1. We then show how we can tune away from coexistence by both tuning V and doping the system. This work paves the way to deploy two-channel MPS+MF theory on some highly demanding high-$T_c$ SC systems, such as 3D arrays of repulsive-U doped Hubbard ladders, where we have recently characterized the properties of such arrays in single-channel MPS+MF calculations. The present approach could thus conclusively show that this SC order would actually be obtained, by explicitly comparing SC against its insulating competitors.

cond-mat.str-el↗

arXiv2022

Transient superconductivity in three-dimensional Hubbard systems by combining matrix product states and self-consistent mean-field theory

We combine matrix-product state (MPS) and Mean-Field (MF) methods to model the real-time evolution of a three-dimensional (3D) extended Hubbard system formed from one-dimensional (1D) chains arrayed in parallel with weak coupling in-between them. This approach allows us to treat much larger 3D systems of correlated fermions out-of-equilibrium over a much more extended real-time domain than previous numerical approaches. We deploy this technique to study the evolution of the system as its parameters are tuned from a charge-density wave (CDW) phase into the superconducting (SC) regime, which allows us to investigate the formation of transient non-equilibrium SC. In our ansatz, we use MPS solutions for chains as input for a self-consistent time-dependent MF scheme. In this way, the 3D problem is mapped onto an effective 1D Hamiltonian that allows us to use the MPS efficiently to perform the time evolution, and to measure the BCS order parameter as a function of time. Our results confirm previous findings for purely 1D systems that for such a scenario superconductivity forms in a transient state.

cond-mat.str-el↗

arXiv2022

Solving 2D and 3D lattice models of correlated fermions -- combining matrix product states with mean field theory

Correlated electron states are at the root of many important phenomena including unconventional superconductivity (USC), where electron-pairing arises from repulsive interactions. Computing the properties of correlated electrons, such as the critical temperature $T_c$ for the onset of USC, efficiently and reliably from the microscopic physics with quantitative methods remains a major challenge for almost all models and materials. In this theoretical work we combine matrix product states (MPS) with static mean field (MF) to provide a solution to this challenge for quasi-one-dimensional (Q1D) systems: Two- and three-dimensional (2D/3D) materials comprised of weakly coupled correlated 1D fermions. This MPS+MF framework for the ground state and thermal equilibrium properties of Q1D fermions is developed and validated for attractive Hubbard systems first, and further enhanced via analytical field theory. We then deploy it to compute $T_c$ for superconductivity in 3D arrays of weakly coupled, doped and repulsive Hubbard ladders. The MPS+MF framework thus enables the reliable, quantitative and unbiased study of USC and high-$T_c$ superconductivity - and potentially many more correlated phases - in fermionic Q1D systems from microscopic parameters, in ways inaccessible to previous methods. It opens the possibility of designing deliberately optimized Q1D superconductors, from experiments in ultracold gases to synthesizing new materials.

cond-mat.str-el↗

arXiv2021

Superconducting pairing from repulsive interactions of fermions in a flat-band system

Fermion systems with flat bands can boost superconductivity by enhancing the density of states at the Fermi level. We use quasiexact numerical methods to show that repulsive interactions between spinless fermions in a one-dimensional (1D) flat-band system, the Creutz ladder, give a finite pairing energy that increases with repulsion, though charge quasi-order (QO) remains dominant. Adding an attractive component shifts the balance in favor of superconductivity and the interplay of two flat bands further yields a remarkable enhancement of superconductivity, well outside of known paradigms for 1D fermions.

cond-mat.str-el↗

arXiv2021

Monolayer CrCl$_3$ as an ideal Test Bed for the Universality Classes of 2D Magnetism

The monolayer halides CrX$_3$ (X=Cl, Br, I) attract significant attention for realizing 2D magnets with genuine long-range order (LRO), challenging the Mermin-Wagner theorem. Here, we show that monolayer CrCl$_3$ has the unique benefit of exhibiting tunable magnetic anisotropy upon applying a compressive strain. This opens the possibility to use CrCl$_3$ for producing and studying both ferromagnetic and antiferromagnetic 2D Ising-type LRO as well as the Berezinskii-Kosterlitz-Thouless (BKT) regime of 2D magnetism with quasi-LRO. Using state-of-the-art density functional theory, we explain how realistic compressive strain could be used to tune the monolayer's magnetic properties so that it could exhibit any of these phases. Building on large-scale quantum Monte Carlo simulations, we compute the phase diagram of strained CrCl$_3$, as well as the magnon spectrum with spin-wave theory. Our results highlight the eminent suitability of monolayer CrCl$_3$ to achieve very high BKT transition temperatures, around 50 K, due to their singular dependence on the weak easy-plane anisotropy of the material.

cond-mat.str-el↗

arXiv2020

Dimensional crossover and phase transitions in coupled chains: Density matrix renormalization group results

Quasi-one-dimensional (Q1D) systems, i.e., three- and two-dimensional (3D/2D) arrays composed of weakly coupled one-dimensional lattices of interacting quantum particles, exhibit rich and fascinating physics. They are studied across various areas of condensed matter and ultracold atomic lattice-gas physics, and are often marked by dimensional crossover as the coupling between one-dimensional systems is increased or temperature decreased, i.e., the Q1D system goes from appearing largely 1D to largely 3D. Phase transitions occurring along the crossover can strongly enhance this effect. Understanding these crossovers and associated phase transitions can be challenging due to the very different elementary excitations of 1D systems compared to higher-dimensional ones. In the present work, we combine numerical matrix product state (MPS) methods with mean-field (MF) theory to study paradigmatic cases of dimensional crossovers and the associated phase transitions in systems of both hard-core and soft-core lattice bosons, with relevance to both condensed matter physics and ultracold atomic gases. We show that the superfluid-to-insulator transition is a first order one, as opposed to the isotropic cases and calculate transition temperatures for the superfluid states, finding excellent agreement with analytical theory. At the same time, our MPS+MF approach keeps functioning well where the current analytical framework cannot be applied. We further confirm the qualitative and quantitative reliability of our approach by comparison to exact quantum Monte Carlo calculations for the full 3D arrays.

cond-mat.str-el↗

arXiv2019

Understanding repulsively mediated superconductivity of correlated electrons via massively parallel DMRG

The so-called minimal models of unconventional superconductivity are lattice models of interacting electrons derived from materials in which electron pairing arises from purely repulsive interactions. Showing unambiguously that a minimal model actually can have a superconducting ground state remains a challenge at nonperturbative interactions. We make a significant step in this direction by computing ground states of the 2D \mbox{U-V} Hubbard model - the minimal model of the quasi-1D superconductors - by parallelized DMRG, which allows for systematic control of any bias and that is sign-problem-free. Using distributed-memory supercomputers and leveraging the advantages of the \mbox{U-V} model, we can treat unprecedented sizes of 2D strips and extrapolate their spin gap both to zero approximation error and the thermodynamic limit. Our results for the spin gap are shown to be compatible with a spin excitation spectrum that is either fully gapped or has zeros only in discrete points, and conversely that a Fermi liquid or magnetically ordered ground state is incompatible with them. Coupled with the enhancement to short-range correlations that we find exclusively in the $d_{xy}$ pairing-channel, this allows us to build an indirect case for the ground state of this model having superconducting order in the full 2D limit, and ruling out the other main possible phases, magnetic orders and Fermi liquids.

cond-mat.str-el↗

arXiv2019

Dynamics of a Mobile Impurity in a Two Leg Bosonic Ladder

We have analyzed the behavior of a mobile quantum impurity in a bath formed by a two-leg bosonic ladder by a combination of field theory (Tomonaga-Luttinger liquid) and numerical (Density Matrix Renormalization Group) techniques. Computing the Green's function of the impurity as a function of time at different momenta, we find a power law decay at zero momentum, which signals the breakdown of any quasi-particle description of the impurity motion. We compute the exponent both for the limits of weak and strong impurity-bath interactions. At small impurity-bath interaction, we find that the impurity experiences the ladder as a single channel one-dimensional bath, but effective coupling is reduced by a factor of $\sqrt 2$, thus the impurity is less mobile in the ladder compared to a one dimensional bath. We compared the numerical results for the exponent at zero momentum with a semi-analytical expression that was initially established for the chain and find excellent agreement without adjustable parameters. We analyze the dependence of the exponent in the transverse hopping in the bath and find surprisingly an increase of the exponent at variance with the naive extrapolation of the single channel regime. We study the momentum dependence of the impurity Green's function and find that, as for the single chain, two different regime of motion exist, one dominated by infrared metatrophy and a more conventional polaronic behavior. We compute the critical momentum between these two regimes and compare with prediction based on the structure factor of the bath. In the polaronic regime we also compute numerically the lifetime of the polaron. Finally we discuss how our results could be measured in cold atomic experiments.

cond-mat.quant-gas↗

arXiv2015

Lattice assisted spectroscopy: a generalized scanning tunnelling microscope for ultra-cold atoms

We show that the possibility to address and image single sites of an optical lattice, now an experimental reality, allows to measure the frequency-resolved local particle and hole spectra of a wide variety of one- and two-dimensional systems of lattice-confined strongly correlated ultracold atoms. Combining perturbation theory and time-dependent DMRG, we validate this scheme of lattice-assisted spectroscopy (LAS) on several example systems, such as the 1D superfluid and Mott insulator, with and without a parabolic trap, and finally on edge states of the bosonic Su-Schrieffer-Heeger model. We also highlight extensions of our basic scheme to obtain an even wider variety of interesting and important frequency resolved spectra.

cond-mat.quant-gas↗

arXiv2015

Minimizing nonadiabaticities in optical-lattice loading

In the quest to reach lower temperatures of ultra-cold gases in optical lattice experiments, non-adiabaticites during lattice loading are one of the limiting factors that prevent the same low temperatures to be reached as in experiments without lattice. Simulating the loading of a bosonic quantum gas into a one-dimensional optical lattice with and without a trap, we find that the redistribution of atomic density inside a global confining potential is by far the dominant source of heating. Based on these results we propose to adjust the trapping potential during loading to minimize changes to the density distribution. Our simulations confirm that a very simple linear interpolation of the trapping potential during loading already significantly decreases the heating of a quantum gas and we discuss how loading protocols minimizing density redistributions can be designed.

cond-mat.quant-gas↗

arXiv2014

Matrix Product State applications for the ALPS project

The density-matrix renormalization group method has become a standard computational approach to the low-energy physics as well as dynamics of low-dimensional quantum systems. In this paper, we present a new set of applications, available as part of the ALPS package, that provide an efficient and flexible implementation of these methods based on a matrix-product state (MPS) representation. Our applications implement, within the same framework, algorithms to variationally find the ground state and low-lying excited states as well as simulate the time evolution of arbitrary one-dimensional and two-dimensional models. Implementing the conservation of quantum numbers for generic Abelian symmetries, we achieve performance competitive with the best codes in the community. Example results are provided for (i) a model of itinerant fermions in one dimension and (ii) a model of quantum magnetism.

cond-mat.str-el↗