I discuss the interplay between non-Fermi liquid behavior and pairing near a quantum-critical point (QCP) in a metal. These tendencies are intertwined in the sense that both originate from the same interaction mediated by gapless fluctuations of a critical order parameter. The two tendencies compete because fermionic incoherence destroys the Cooper logarithm, while the pairing eliminates...
Superconductivity in low carrier density metals challenges the conventional electron-phonon theory due to the absence of retardation required to overcome Coulomb repulsion. Here I will discuss how pairing mediated by energy fluctuations, ubiquitously present close to continuous phase transitions, occurs in dilute quantum critical polar metals and results in a dome-like dependence of the...
Bilayer graphene at certain small internal twist angles develops large scale moiré patterns with flat energy bands hosting correlated insulating states and superconductivity. The large system size and intricate band structure have however hampered investigations into the properties of the superconducting state. By using full-scale atomistic modeling with local electronic interactions,...
Superconductivity is abundant near quantum-critical points, where fluctuations suppress the formation of Fermi liquid quasiparticles and the Bardeen-Cooper-Schrieffer theory no longer applies. Two very distinct approaches have been developed to address this issue: quantum-critical Eliashberg theory and holographic superconductivity. The former includes a strongly retarded pairing interaction...
Local three- and four-point correlators yield important insight into strongly correlated systems and have many applications. However, the nonperturbative, accurate computation of dynamical multipoint correlators is challenging, particularly in the real-frequency domain for systems at low temperatures. We have developed generalized spectral representations for multipoint correlators, and a...
The many-body problem is usually approached from one of two perspectives: the first originates from an action and is based on Feynman diagrams, the second is centered around a Hamiltonian and deals with quantum states and operators. The connection between results obtained in either way is made through spectral (or Lehmann) representations, well known for two-point correlators. We have derived...
In recent years, reliable approaches have been developed [1,2] to unambiguously identify the dominant fluctuations driving the multifaceted phenomena of many-electron physics. Among those, the "fluctuation diagnostics" [3] relies on the possibility of expressing the physical quantity of interest in complementary representations. Hitherto, this scheme has been only applied to normal,...
In the last 30 years, the dynamical mean field theory (DMFT) has developed to a standard tool for the theoretical description of strongly correlated electron systems. It self-consistently maps a lattice Hamiltonian onto an impurity problem which can be solved exactly via exact diagonalization or Quantum Monte Carlo methods. In this way, all purely local correlation effects in the system are...
Experiments in cold atom systems see identical signatures of many body localisation (MBL) in both one-dimensional (d=1) and two-dimensional (d=2) systems despite the thermal avalanche hypothesis showing that the MBL phase is unstable for d>1. Underpinning the thermal avalanche argument is the assumption of exponential localisation of local integrals of motion (LIOMs), a result taken from the...
Recent experimental observations of correlated phases in magic-angle twisted bilayer graphene (MATBG) strongly indicate the enhanced importance of electronic correlations in this flat band system. Twist in graphene layers in MATBG results in the formation of moiré patterns with length scales much larger than the atomic distance between carbon atoms in individual layers. It is often believed...
We analyse the competition of antiferromagnetism and superconductivity in the two -dimensional Hubbard model at moderate coupling. By using the functional renormalization group in its fully dynamical implementation, we compute the flow of the vertex function and of the magnetic and superconducting order parameters. In spite of strong frequency dependences of the effective interations and the...
The presence of multiple bands qualitatively changes the nodal structure of an inversion-symmetric time-reversal symmetry-breaking superconductor. Instead of point or line nodes, the gap exhibits extended nodal pockets, called Bogoliubov Fermi surfaces [1-4]. These surfaces originate from the “inflation” of point and line nodes in the absence of time-reversal symmetry breaking. In this work...
Analog models provide another point of view to approach problems. They play a very important role in physics and mathematics, since they allow us to study and observe phenomena that are not directly accessible. In this talk, we will address the problem of cosmological particle production in curved and expanding universes, specifically, in expanding Friedmann-Lemaître-Robertson-Walker (FLRW)...
Today there exists a strong research focus on topological effects in condensed matter. Initial studies were only focused on non-interacting electronic systems, but attention is now shifting towards the influence of electron-electron interactions and also the broken symmetry states they can generate. Real-world materials bring disorder as a third important component, as many symmetry broken...
The study of charge excitations in cuprate superconductors is an active topic in present days. Recent resonant inelastic x-ray scattering (RIXS) experiments detected low-energy plasmons in electron-doped (e-cuprates) and hole-doped (h-cuprates) cuprates. These plasmon excitations are, in leading order of a $1/N$ approximation, satisfactorily described in the context of the layered $t$-$J$...
We showcase several fundamental characteristics of the multiloop functional renormalization group (mfRG) flow by hands of its application to a prototypical many-electron system: the Anderson impurity model (AIM). On the one hand, we analyze the convergence of the algorithm in the different parameter regions of the AIM. On the other hand, by exploiting the converged results, we inspect the...
We study variants of the two-leg t-J ladder at low fillings using matrix
product states (MPS) and analytical methods. While the groundstate phase
diagram for the usual t-J ladder with spatially isotropic couplings at
fillings $n>0.5$ has been studied in detail, relatively little is known
at low fillings. We address the phase diagram at low fillings and
investigate the influence of...
Heavy-fermion systems [1] have triggered a tremendous amount of experimental and theoretical research since the discovery of quantum criticality and pronounced non-Fermi-liquid behavior in these materials more than two decades ago.
The properties of these compounds are largely derived from localized f orbitals hybridized with broad conduction bands, resulting in a lattice of local moments...
Electronic correlations are often discussed in terms of effective low-energy models, with the Hubbard model as the most prominent example. To simulate real materials, the Coulomb interaction U needs to be determined, taking into account the screening by high-energy electronic states. The constrained Random Phase Approximation (cRPA) is frequently used for this purpose, but its applicability...
Instanton Crystal is a fascinating phase which is encountered when the minimum of the free energy corresponds to a configuration with an imaginary-time-dependent order parameter in the form of a chain of alternating instantons and anti-instantons. An important feature of this phase is that the average of the order parameter over the imaginary time vanishes [1].
We propose a model that hosts...
We investigate the phase diagram of the unfrustrated triangular lattice Hubbard model in a center-focused cellular dynamical mean-field theory (CDMFT) approach using impurity clusters of 4, 7 and 19 sites. We investigate the Mott metal-to-insulator transition and crossover region in terms of these cluster sizes. Using a magnetic symmetry-broken approach of the CDMFT, allowing for a rotations...
The discovery of superconductivity in hole-doped infinite-layer NdNiO$_2$ — a transition metal oxide that is both isostructural and isoelectronic to cuprate superconductors — has lead to renewed enthusiasm in the hope of understanding the origin of unconventional superconductivity. In this talk, we present the many body wavefunction analysis of electron-removal (which mimics hole-doping)...
Current in conventional conductors is characterized by electron-impurity and electron-phonon scattering. However, recent breakthroughs in fabrication of 2D materials with very low impurity has led to the realization of a new regime of transport, namely, the hydrodynamic regime, where electron-electron Coulomb interaction dominates. A lot of work has been done recently on hydrodynamic transport...
We analyse the effect of multiloop corrections in the 2D Attractive Hubbard Model. In a TU-fRG scheme where the conventional multi-loop self-energy flow equations are replaced with a Schwinger-Dyson flow, we demonstrate the importance of self-energy iteration in the convergence to reference Parquet results. Furthermore, we study the feedback of the s-wave pairing fluctuations on the charge...
We present a multiloop pseudofermion functional renormalization group
(pffRG) approach to quantum spin systems and its application to the
spin-1/2 Heisenberg model on the kagome lattice. At pure
nearest-neighbor coupling, the system shows indications for an algebraic
spin liquid through slower-than-exponential decay with distance for the
static spin susceptibility, while the pseudofermion...
The computation of the frequency-dependent conductivity in interacting systems is still an open problem while being one of the most widely used experimental techniques. Even restricting the question to the zero-frequency limit, there remain unsolved questions such as the nature of the linear dependence of the dc resistivity in multiple strongly-correlated materials ranging from cuprates to...
Propagators and associated diagrammatic equations are the bedrock upon which a large portion of qunatum many-body theory is built. For one-particle physics, the imaginary-time axis combined with recently developed, maximally compact intermediate representation (IR) allows fast and stable computations. However, in capturing fluctuations and phase transitions, the two-particle propagator takes...
In this work we probe and contrast different measures of entanglement for quantum systems, the most well-known of which is the von Neumann entropy. The entropy, however, is only a good measure of entanglement when a system is in a pure state. For mixed states other measures exist such as the concurrence, the Entanglement of Formation, and Negativity. We choose to study a model Hamiltonian...
As an example of quantum criticality on a compressible lattice we study the Lorentz invariant φ^4 theory with an N-component field φ, where strain couples to the square of the order parameter. In three spatial dimensions this coupling as well as the self-interaction of the φ field are both marginal on the tree-level. We compute the one-loop renormalization group equations treating the φ field...
Geometric concepts provide a very fruitful language for quantum (interband) contributions to the dc electrical conductivity of multiband systems. A well-known example is the intrinsic anomalous Hall conductivity, which is based on the Berry curvature. The quantum metric is a second central quantity of band theory but has so far not been related to many response coefficients due to its...
Building on the results in arxiv:2103.03895, we develop a renormalization group theory to understand the localization phase diagrams of 1D quasiperiodic lattice models, using commensurate approximants. We define renormalized couplings that measure the dependence of single-particle energies on phase twists/Bloch momenta and real-space shifts for increasing unit cell size.
We show that for...
We present a multiloop implementation of the functional renormalization group (fRG) based on the single boson exchange (SBE) decomposition applied to the two dimensional Hubbard model.
In the SBE diagrams of the two particle vertex are classified accoring to their reducibility in the bare interaction compared to the two-particle reducibility of the widely-used parquet decomposition. This...
We illustrate the computational advantages of the recently introduced single-boson exchange (SBE) formulation for the one-loop functional renormalization group (fRG) applied to the two-dimensional Hubbard model. We present a detailed analysis of the screened interactions and Yukawa couplings and their evolution with temperature and interaction strength, both at half filling and finite doping....
We analyze the properties of magnons in metallic electron systems with spiral magnetic order. Our analysis is based on the random phase approximation for the susceptibilities of tight binding electrons with a local Hubbard interaction in two or three dimensions. We identify three magnon branches from poles in the susceptibilities, one associated with in-plane, the other two associated with...
Several quantum spin liquid candidate materials, such as 𝛼RuCl3 and
1T-TaSe2, are exfoliable, so that it is possible to investigate 2D samples
which avoid the manifestation of bulk properties that might disrupt the
quantum spin liquid phase. In this phase the material is a Mott insulator impenetrable to direct electric probes such as charge currents.
Despite this, we propose an...
Frustrated three-dimensional quantum magnets bear a rich phenomenology but are notoriously hard to treat theoretically. We show how a SO(3) Majorana representation of spin operators, in combination with the functional renormalization group allows for quantitative simulations at finite temperatures. Focusing on Heisenberg magnets, we establish a finite-size scaling approach and extract critical...
Dissipative quantum impurity models represent conceptually simple yet non-trivial settings for quantum criticality. Here we consider the SU(2)-symmetric spin-boson (or Bose-Kondo) model with a power-law bath spectrum $\propto \omega^s$, relevant to diverse problems such as cavity quantum electrodynamics, magnetic moments in quantum critical magnets, and Kondo-breakdown transitions in...
A multitude of novel phases have been proposed for twisted bilayer graphene (TBG) at charge neutrality such as a nematic insulator which breaks C3 lattice symmetry or as inter-valley coherent order (IVC) which breaks U(1) valley symmetry. We show that the Dirac fermion model of TBG is invariant under an SU(4) group composed of combined spin, valley and sublattice transformations. We determine...
The development of twisted bilayer TMDs established a new field for the investigation of correlated electron phases in 2D materials on triangular lattices. Compared to TBG, twisted bilayer TMDs allow the access to quantitative different layer orientations with respect to the twisting angle. This results in the case of AB stacking to a suppressed interlayer tunneling from the bottom to the top...
While bulk 2H-NbSe2 is generally accepted to be a conventional superconductor, several unconventional features of the superconducting state have been reported in the monolayer limit, including the breaking of threefold symmetry in magnetotransport [1,2] and anomalously large in-plane critical fields [3]. In this work, I will first present another unconventional feature measured by our...
The generalized Dynamical Mean Field Theory (DMFT) susceptibility is (formally) derived from the response of the physical system to a small perturbation of the lattice Hamiltonian. The perturbation couples the lattice to an external environment, which allows for the transfer of both momentum and energy. In this setting, the eigenvectors of the generalized susceptibility can be interpreted as a...
We study the half-filled two-dimensional Hubbard model on a square lattice in cellular dynamical mean-field theory (CDMFT), a real-space cluster extension [1] of the dynamical mean-field theory. By increasing the number of cluster sites up to 6x6 we observe a progressive reduction of the onset interaction U* of a metal-insulator crossover. In particular, in the case of 4x4 sites, we observe a...
We investigate the role of non-local electronic correlations at finite temperatures in the half-filled triangular lattice Hubbard model using the dynamical vertex approximation (DΓA), a diagrammatic extension [1] of the dynamical mean-field theory (DMFT). We analyze the impact of (quantum) phase transitions on finite temperature properties at the one- and two-particle level. We discuss the...
SmB$_6$ is a mixed valence compound and a well known candidate material for topological Kondo insulators. With the application of pressure the valence of Sm atoms increases and as a consequence antiferromagnetism emerges in experiments.
We have constructed a tight-binding model to describe the system after the spin exciton mode has condensed into one out of two possible antiferromagnetic...
The semiconducting diode, which is characterized by a highly asymmetric current-voltage relation, is central to modern-day electronics. In the last few years, its superconducting analogue – a system that behaves like a superconductor for current flow in one direction but exhibits finite resistance when the current direction is reversed – has attracted attention in the physics community, due to...
Quantum spin liquid (QSL), an exotic magnetic phase with fractionalized spin excitations and intricate entanglement structure, has been pursued both theoretically and experimentally since its first proposal by Anderson in 1973. Theoretical models and candidate materials with strong geometrical or exchange frustration are expected to greatly reduce the ordering temperature and reveal the...
In frustrated magnets, novel phases characterized by fractionalized excitations and emergent gauge fields can occur. A paradigmatic example is given by the Kitaev model of localized spins 1/2 on the honeycomb lattice, which realizes an exactly solvable quantum spin liquid ground state with Majorana fermions as low-energy excitations. I will demonstrate that the Kitaev solution can be...
I will present some results showing that the Hubbard repulsion and other interactions like the Hund's coupling and electron-phonon interaction can either compete or cooperate, leading to different strongly correlated phases.
First I will review the interplay between Hubbard U and Hund's coupling emphasizing how different fillings are characterized by different scenarios. Namely at...
The Kondo
lattice model
plays a key role in our
understanding of quantum materials,
but a lack of small parameters has posed a
long-standing problem. We
present a 3 dimensional
S$=1/2$ Kondo lattice model describing a spin liquid within an
electron sea. Strong correlations in the spin liquid
are treated exactly, enabling a controlled analytical approach. The
solution...
I will first review why it is important to disentangle the effects of electronic interactions and electron-lattice interactions in unconventional metals. I will then describe an observable process that depends crucially on electron-lattice interactions: the transfer of energy from hot electrons to a cooler lattice. Textbook discussion of this effect build upon weakly interacting electronic...
We study hydrodynamic electron transport in Corbino and Hall bar graphene devices. In Corbino geometry due to the irrotational character of the flow, the forces exerted on the electron liquid are expelled from the bulk. We show that in the absence of Galilean invariance, force expulsion produces qualitatively new features in thermoelectric transport: (i) it results in drops of both voltage and...
A vison is an excitation of the Kitaev spin liquid which carries a $\mathbb Z_2$ gauge flux. While immobile in the pure Kitaev model, it becomes a dynamical degree of freedom in the presence of perturbations. We [1] study an isolated vison in the isotropic Kitaev model perturbed by a small external magnetic field h, an offdiagonal exchange interactions Γ and a Heisenberg coupling J. In the...
The realization of correlated insulators and superconductivity in twisted van der Waals heterostructures has brought forth twisting as a new control knob in condensed matter laboratories. In this talk we will show how twisting can be used to control the low energy physics of bilayers of nodal superconductors. Focusing in the vicinity of the Dirac nodes in their Bogolioubov de Gennes (BdG)...
Recent experimental progress has brought about better, defect-free infinite-layer nickelates [1] and the first finite-layer nickelate superconductor [2]. The measured superconducting dome is in exceedingly good agreement with our theoretical prediction [3] based on single Ni-$d_{x^2-y^2}$-band Hubbard model plus a decoupled electron reservoir for the pockets around the $A$ momentum and at low...
The different low energy effective Hamiltonians for cuprate high-Tc superconductors [1] can be considered as steps in a Wilsonian renormalization procedure from large- to small energy windows around the Fermi level. High energy models include bare interactions and all spin-, orbital-, and lattice degrees of freedom explicitly. However, at low energies many researchers consider the single band...
The recent discovery of AV$_3$Sb$_5$ (A=K,Rb,Cs) has uncovered an intriguing arena for exotic Fermi surface instabilities in kagome metals. Aside from charge density wave order, a multi-dome superconducting phase is found, with strong indications to be of unconventional origin including features such as time reversal symmetry breaking. We find that the sublattice interference mechanism is...
I will present recent numerically exact finite-temperature results for the two-dimensional Hubbard model obtained by diagrammatic Monte Carlo. I will show that there are several correlation regimes characterized by different magnetic correlation lengths and interaction strengths. I will discuss the connection between these regimes and the onset of a pseudogap. Finally, I will try to shake...
Order Fractionalization and Neutral Fermi Surfaces.
Piers Coleman*
Center for Materials Theory, Physics and Astronomy, Rutgers University
Department of Physics, Royal Holloway University London.
Over the past two decades, research into quantum materials has reverberated
under the impact of new concepts, particularly those of topology and
fractionalization. This talk will discuss...
The discovery of near-Room-Temperature Superconductivity in High-Pressure Superhydrides
has revolutionized the landscape of superconducting material research, establishing ab-initio calculations as the tool of choice for predicting superconducting properties and synthesis conditions
of new superconductors. [1]
In this talk, I will give an overview of our recent efforts to design high-Tc...
Experimental demonstrations of tunable correlation effects in magic-angle twisted bilayer graphene have put two-dimensional moiré quantum materials at the forefront of condensed-matter research. In particular, bilayers of transition metal dichalcogenides (TMDs) have further enriched the opportunities for analysis and utilization of correlations in such systems. Recently, within the latter...
The recent technological development of THz spectroscopy makes it possible to probe properties of quantum matter, which cannot be observed in equilibrium. This is of considerable interest in the field of nematic unconventional superconductors, where controlled probing of the non-equilibrium dynamics yields access to understanding ground state properties of the underlying system.
In the first...
We introduce a strong coupling dual super-perturbation scheme starting from the general reference system optimised for a given many-body problem. We discuss the physics of high-temperature cuprate superconductors starting from the highly degenerate four-site plaquette of the Hubbard model as a reference system. The degeneracy causes strong fluctuations when a lattice of plaquettes is...
In the recent literature, the concept of topological Mott insulator has been spelled out in quite different ways. Most of the proposed realizations rely either on Hartree-Fock approximations or on appropriately defined auxiliary degrees of freedom. I will discuss a novel, remarkably simple way of describing a topological Mott insulator without long-range order based on the topological...
Leveraging the power of algorithmic Matsubara integration (AMI) we can generate pseudo-analytic results for virtually any diagrammatic expansion. Here we generate the longitudinal spin and charge susceptibilities for the 2D Hubbard model and employ our AMI toolset to obtain expressions that are explicit functions of chemical potential, temperature, interaction strength and frequency (both...
Using appropriate terminology, we say more with fewer words. A useful terminology to describe two-particle electronic correlations was introduced by Hedin [1] and in the context of the spin-fermion model [2,3]. In this spirit, we show that re-expressing two-particle correlations through exchange bosons [4,5] greatly enhances the computational power of algorithms and, at the same time, gives us...
