arXiv subjects

Nick Bultinck

Publications and source records attributed to Nick Bultinck.

At least 19 recordsLinked to original sources

arXiv2026

Superconductivity from emergent dipolar interactions in a fractionalized Fermi liquid

Starting from the spin-fermion model or Hertz-Millis theory describing electrons coupled to anti-ferromagnetic spin fluctuations we develop a theory to describe the transition from a fractionalized Fermi liquid into a $d_{x^2-y^2}$ superconductor. We focus on small electron doping on top of the half-filled state. The doped electrons enter the system as spinon-chargon bound states, which form a small, reconstructed Fermi surface. The bound states are neutral under the emergent U(1) gauge symmetry of the fractionalized Fermi liquid, but interact via a dipolar two-body potential. We show that because of the projective action of translation symmetry on the spinons and chargons, the Fourier components of this repulsive dipolar interaction are peaked at the anti-ferromagnetic wave vector, thereby providing a robust microscopic mechanism for $d_{x^2-y^2}$ pairing in a fractionalized metal.

cond-mat.supr-con↗

arXiv2026

Quantum Monte Carlo fermion spectroscopy of a non-compact CP$^1$ model

We study a model describing electrons coupled to anti-ferromagnetic spin fluctuations, and consider the situation where hedgehog defects in the order parameter field are suppressed. Without hedgehogs, the bosonic sector of the theory can be taken to realize the physics of the non-compact CP$^1$ theory with a deconfined U$(1)$ gauge field. After strongly coupling the boson to fermion spins, we simulate the single-particle spectral properties of a hedgehog-suppressed electron-boson model defined on a bilayer square lattice with Quantum Monte Carlo, and interpret the results in terms of an effective theory with fractionalized spinon and chargon excitations. As one of our main results we show that the electron gap on top of the half-filled insulator with gapless photon fluctuations closely resembles the mean-field dispersion of an electron in an anti-ferromagnetic spin background, even though the system fully preserves both the translation and spin rotation symmetry. Finally, we discuss potential implications of our results for the high-temperature superconductors.

cond-mat.str-el↗

arXiv2026

Lowering the temperature of two-dimensional fermionic tensor networks with cluster expansions

Representing the time-evolution operator as a tensor network constitutes a key ingredient in several algorithms for studying quantum lattice systems at finite temperature or in a non-equilibrium setting. For a Hamiltonian composed of strictly short-ranged interactions, the Suzuki-Trotter decomposition is the main technique for obtaining such a representation. In [B.~Vanhecke, L.~Vanderstraeten and F.~Verstraete, Physical Review A, L020402 (2021)], an alternative strategy, the cluster expansion, was introduced. This approach naturally preserves internal and lattice symmetries and can more easily be extended to higher-order representations or longer-ranged interactions. We extend the cluster expansion to two-dimensional fermionic systems, and employ it to construct projected entangled-pair operator (PEPO) approximations of Gibbs states. We also discuss and benchmark different truncation schemes for multiplying layers of PEPOs together. Applying the resulting framework to a two-dimensional spinless fermion model with attractive interactions, we resolve a clear phase boundary at finite temperature.

cond-mat.str-el↗

arXiv2025

Mean-field Modelling of Moir\'e Materials: A User's Guide with Selected Applications to Twisted Bilayer Graphene

We review the theoretical modelling of moir\'e materials, focusing on various aspects of magic-angle twisted bilayer graphene (MA-TBG) viewed through the lens of Hartree-Fock mean-field theory. We first provide an elementary introduction to the continuum modelling of moir\'e bandstructures, and explain how interactions are incorporated to study correlated states. We then discuss how to implement mean-field simulations of ground state structure and collective excitations in this setting. With this background established, we rationalize the power of mean-field approximations in MA-TBG, by discussing the idealized "chiral-flat" strong-coupling limit, in which ground states at electron densities commensurate with the moir\'e superlattice are exactly captured by mean-field ans\"atze. We then illustrate the phenomenological shortcomings of this limit, leading us naturally into a discussion of the intermediate-coupling incommensurate Kekul\'e spiral (IKS) order and its origins in ever-present heterostrain. IKS and its placement within an expanded Hartree-Fock manifold form our first "case study". Our second case study involves time-dependence, and focuses on the collective modes of various broken-symmetry insulators in MA-TBG. As a third and final case study, we return to the strong-coupling picture, which can be stabilized by aligning MA-TBG to an hBN substrate. In this limit, we show how mean field theory can be adapted to the translationally non-invariant setting in order to quantitatively study the energetics of domain walls in orbital Chern insulating states. We close with a discussion of extensions and further applications. Used either as a standalone reference or alongside the accompanying open-source code, this review should enable readers with a basic knowledge of band theory and many-body physics to systematically build and analyze detailed models of generic moir\'e systems.

cond-mat.str-el↗

arXiv2025

Multi-Q spin-valley order in twisted WSe2

We report on a study of the interacting phase diagram of $3.65^\circ$-twisted WSe$_2$ at moir\'e hole filling $\nu=1$, in which we find previously-overlooked types of magnetism. Specifically, in part of the phase diagram we obtain a magnetic order parameter which modulates in space with four different non-zero wave vectors, corresponding to the three $M$-points and one $K$-point of the moir\'e Brillouin zone. These multi-Q orders, which can be coplanar or non-coplanar, are continuous deformations of the $120^\circ$ spin-valley anti-ferromagnet (AFM), where the unit cell has expanded by a factor of four. Interestingly, we find that the multi-Q states are stabilized for experimentally relevant values of interaction strength and displacement field, and are accompanied by a softening of the spin fluctuations near the $M$-points of the moir\'e

cond-mat.str-el↗

arXiv2025

Putting a new spin on the incommensurate Kekulé spiral: from spin-valley locking and collective modes to fermiology and implications for superconductivity

We revisit the global phase diagram of magic-angle twisted bilayer and [symmetric] trilayer graphene (MA-TBG/TSTG) in light of recent scanning tunneling microscopy (STM) measurements on these materials. These experiments both confirmed the importance of strain in stabilizing the predicted incommensurate Kekulé spiral (IKS) order near filling $|ν|=2$ of the weakly dispersive central bands in both systems, and suggested a key role for electron-phonon couplings and short-range Coulomb interactions in selecting between various competing orders at low strain in MA-TBG. Here, we show that such interactions $\textit{also}$ play a crucial role in selecting the spin structure of the strain-stabilized IKS state. This in turn influences the visibility of the IKS order in STM in a manner that allows us to infer their relative importance. We use this insight in conjunction with various other pieces of experimental data to build a more complete picture of the phase diagram, focusing on the spectrum of low-lying collective modes and the nature of the doped Fermi surfaces. We explore the broad phenomenological implications of these results for superconductivity.

cond-mat.str-el↗

arXiv2025

Strange metal and Fermi arcs from disordering spin stripes

We revisit the effective theory for fluctuating spin stripes coupled to a Fermi surface, and consider the parameter regime where a spin nematic phase intervenes between the spin density wave state and the symmetric state. It is shown that adding potential disorder to this theory, which acts as an unconventional type of random-field disorder, naturally gives rise to a phase diagram containing a quantum critical point that is described by the universal theory of strange metals with spatial disorder in both the magnitude and sign of the electron-boson coupling term [A.A. Patel, H. Guo, I. Esterlis and S. Sachdev, Science 381, 790 (2023)]. One difference compared to the original theory, however, is that at non-zero temperatures the disordered spin-stripe model automatically self-averages over the sign of the coupling. We also study the effects of thermal fluctuations in a phenomenological model for the disordered spin density wave state, and find from Monte Carlo simulations that a short anti-ferromagnetic correlation length (order 4-5 lattice constants) already leads to pronounced Fermi arcs in the electronic spectral weight.

cond-mat.str-el↗

arXiv2025

Valence-bonds, spin liquids and unconventional criticality in a 1D Kondo insulator

We consider a one-dimensional multi-orbital Kondo lattice model and show that by tuning the kinetic energy of the itinerant electrons it is possible to stabilize Kondo insulators with non-trivial spin physics. In particular, depending on the size of the exchange coupling between the local moments, we find kinetic-energy-driven transitions between a featureless Kondo insulator and a valence-bond solid or a gapless spin liquid. We also provide evidence for an unconventional continuous phase transition between two featureless Kondo insulators distinguished by their quantum numbers under reflection symmetry.

cond-mat.str-el↗

arXiv2025

Extracting average properties of disordered spin chains with translationally invariant tensor networks

We develop a tensor network-based method for calculating disorder-averaged expectation values in random spin chains without having to explicitly sample over disorder configurations. The algorithm exploits statistical translation invariance and works directly in the thermodynamic limit. We benchmark our method on the infinite-randomness critical point of the random transverse field Ising model.

cond-mat.dis-nn↗

arXiv2025

Constraints from anti-unitary symmetries on phase diagrams of sign problem-free models

A powerful way to guarantee the absence of a sign problem in determinantal quantum Monte Carlo simulations is imposing a particular type of anti-unitary symmetries. It is shown that these same symmetries give rise to constraints on correlation functions, which can be used to identify local operators whose correlations upper bound those of a large class of physically relevant operators, including for example superconducting order parameters. Our results also help understand why it is difficult to realize generic finite-momentum orders in sign problem-free models.

cond-mat.str-el↗

arXiv2025

First-Principles Evidence for Strongly Correlated Superconductivity Driven by Structural Variations in La$_3$Ni$_2$O$_7$

We conduct first-principles simulations of La$_3$Ni$_2$O$_7$, a nickelate in which recent experiments have shown signs of high-temperature superconductivity. Within the hydrostatic pressure range where superconductivity is observed, we find a significant increase in effective on-site repulsion in the maximally localised Wannier functions comprising the Ni $e_g$ bands crossing the Fermi energy. We attribute this increase to an interplay between orbital localisation and competing screening channels arising from structural variations. Our results indicate that the superconducting region in the La$_3$Ni$_2$O$_7$ phase diagram coincides with a region of enhanced electronic correlations, which show a close correspondence with the critical temperature. Including finite temperatures up to 100 K, $ab$ $initio$ molecular dynamics simulations then provide new insights into the debated structural phase diagram and further clarify the origin of the right-triangular superconducting dome. Finally, we study Ac$_3$Ni$_2$O$_7$ to confirm the crucial role of the $A$-site cation in shaping the pressure-driven evolution of electronic correlations.

cond-mat.supr-con↗

arXiv2024

Fermionic tensor network methods

We show how fermionic statistics can be naturally incorporated in tensor networks on arbitrary graphs through the use of graded Hilbert spaces. This formalism allows to use tensor network methods for fermionic lattice systems in a local way, avoiding the need of a Jordan-Wigner transformation or the explicit tracking of leg crossings by swap gates in 2D tensor networks. The graded Hilbert spaces can be readily integrated with other internal and lattice symmetries in tensor networks, and only require minor extensions to an existing tensor network software package. We review and benchmark the fermionic versions of common algorithms for matrix product states and projected entangled-pair states.

quant-ph↗

arXiv2024

Textured Exciton Insulators

We introduce and study new interacting topological states that arise in time-reversal symmetric bands with an underlying obstruction to forming localized states. If the $U(1)$ valley symmetry linked to independent charge conservation in each time-reversal sector is spontaneously broken, the corresponding `excitonic' order parameter is forced to form a topologically non-trivial texture across the Brillouin zone. We show that the resulting phase, which we dub a textured exciton insulator, cannot be given a local-moment description due to a form of delicate topology. Using toy models of bands with Chern or Euler obstructions to localization we construct explicit examples of the Chern or Euler texture insulators (CTIs or ETIs) they support, and demonstrate that these are generically competitive ground states at intermediate coupling. We construct field theories that capture the response properties of these new states. Finally, we identify the incommensurate Kekul\'e spiral phase observed in magic-angle bi- and trilayer graphene as a concrete realization of an ETI.

cond-mat.str-el↗

arXiv2024

Chern-Textured Exciton Insulators with Valley Spiral Order in Moir\'e Materials

We explore the phase diagrams of moir\'e materials in search of a new class of intervalley-coherent correlated insulating state: the Chern texture insulator (CTI). This phase of matter, proposed in a companion paper, breaks valley $U(1)$ symmetry in a nontrivial fashion wherein the valley order parameter is forced to texture in momentum space as a consequence of band topology. Using detailed Hartree-Fock studies, we establish that the CTI emerges as an energetically competitive intermediate-coupling ground state in several moir\'e systems which lack a twofold rotation symmetry that forbids the single-particle topology essential to the formation of the CTI valley texture.

cond-mat.str-el↗

arXiv2024

Nodal d-wave pairing from spin fluctuations in a thermally disordered anti-ferromagnet

We consider electron pairing in a two-dimensional thermally disordered itinerant anti-ferromagnet. It is shown that transverse spin fluctuations in such a state can give rise to superconductivity with a sizeable critical temperature $T_c$. Below $T_c$ there is quasi-long-range spin-singlet and $d_{x^2-y^2}$ superconducting order, together with fluctuating triplet order at momentum $(π,π)$. The singlet pairs we find are tightly bound together, and the pair wavefunction has a purely inter-sublattice structure due to the U(1) spin rotation symmetry of the anti-ferromagnet.

cond-mat.supr-con↗

arXiv2024

Hawking radiation on the lattice from Floquet and local Hamiltonian quench dynamics

We construct two free fermion lattice models exhibiting Hawking pair creation. Specifically, we consider the simplest case of a d=1+1 massless Dirac fermion, for which the Hawking effect can be understood in terms of a quench of the uniform vacuum state with a non-uniform Hamiltonian that interfaces modes with opposite chirality. For both our models we find that additional modes arising from the lattice discretization play a crucial role, as they provide the bulk reservoir for the Hawking radiation: the Hawking pairs emerge from fermions deep inside the Fermi sea scattering off the effective black hole horizon. Our first model combines local hopping dynamics with a translation over one lattice site, and we find the resulting Floquet dynamics to realize a causal horizon, with fermions scattering from the region outside the horizon. For our second model, which relies on a purely local hopping Hamiltonian, we find the fermions to scatter from the inside. In both cases, for Hawking temperatures up to the inverse lattice spacing we numerically find the resulting Hawking spectrum to be in perfect agreement with the Fermi-Dirac quantum field theory prediction.

quant-ph↗

arXiv2024

Resurgence of superconductivity and the role of $d_{xy}$ hole band in FeSe$_{1-x}$Te$_x$

Iron-chalcogenide superconductors display rich phenomena caused by orbital-dependent band shifts and electronic correlations. Additionally, they are potential candidates for topological superconductivity due to the band inversion between the Fe $d$ bands and the chalcogen $p_z$ band. Here we present a detailed study of the electronic structure of the nematic superconductors FeSe$_{1-x}$Te$_x$ ($0<x<0.4$) using angle-resolved photoemission spectroscopy to understand the role of orbital-dependent band shifts, electronic correlations and the chalcogen band. We assess the changes in the effective masses using a three-band low energy model, and the band renormalization via comparison with DFT band structure calculations. The effective masses decrease for all three-hole bands inside the nematic phase followed by a strong increase for the band with $d_{xy}$ orbital character. Interestingly, this nearly-flat $d_{xy}$ band becomes more correlated as it shifts towards the Fermi level with increasing Te concentrations and as the second superconducting dome emerges. Our findings suggests that the $d_{xy}$ hole band, which is very sensitive to the chalcogen height, could be involved in promoting an additional pairing channel and increasing the density of states to stabilize the second superconducting dome in FeSe$_{1-x}$Te$_x$. This simultaneous shift of the $d_{xy}$ hole band and enhanced superconductivity is in contrast with FeSe$_{1-x}$S$_x$.

cond-mat.supr-con↗

arXiv2024

Finite-Entanglement Scaling of 2D Metals

We extend the study of finite-entanglement scaling from one-dimensional gapless models to two-dimensional systems with a Fermi surface. In particular, we show that the entanglement entropy of a contractible spatial region with linear size $L$ scales as $S\sim L\log[ξf(L/ξ)]$ in the optimal tensor network, and hence area-law entangled, state approximation to a metallic state, where $f(x)$ is a scaling function which depends on the shape of the Fermi surface and $ξ$ is a finite correlation length induced by the restricted entanglement. Crucially, the scaling regime can be realized with numerically tractable bond dimensions. We also discuss the implications of the Lieb-Schultz-Mattis theorem at fractional filling for tensor network state approximations of metallic states.

cond-mat.str-el↗