# Gapless Fermions - from Fermi liquids to strange metals

For each poster contribution there will be one poster wall (width: 97 cm, height: 250 cm) available. Please do not feel obliged to fill the whole space. Posters can be put up for the full duration of the event.

### Statistics-tuned phases of pseudofermions in one dimension

We show that a quadratic system of pseudofermions, with tunable fractionalized statistics, can host a rich phase diagram on a one-dimensional chain with nearest- and next-nearest-neighbor hopping. Using a combination of numerical and analytical techniques, we show that by varying the statistical angle and the ratio of the hopping, the system stabilizes two Tomonaga-Luttinger liquids (TLL) with central charges c=1 and 2, respectively, along with the inversion symmetry broken bond-ordered (BO) insulating phase. Interestingly, the two quantum phase transitions in the system, (1) between the two TLLs and (2) the c=1 TLL and BO phase, can be engendered by solely tuning the statistics of the pseudofermions. Our analysis shows that both these transitions are continuous and novel with the former lacking a local order-parameter based description and the latter of Berezinskii-Kosterlitz-Thouless type. These phases and phase transitions can be of direct experimental relevance in the context of recent studies of fermionic cold atoms.

### Isolated Zeros Destroy Fermi Surface in Holographic Lattice Models

Balm, Floris

We study the fermionic spectral density in a strongly correlated quantum system described by a gravity dual. In the presence of periodically modulated chemical potential, which models the effect of the ionic lattice, we explore the shapes of the corresponding Fermi surfaces, defined by the location of peaks in the spectral density at the Fermi level. We find that at strong lattice potentials sectors of the Fermi surface are unexpectedly destroyed and the Fermi surface becomes an arc-like disconnected manifold. We explain this phenomenon in terms of a collision of the Fermi surface pole with zeros of the fermionic Green's function, which are explicitly computable in the holographic dual.

### Spin-phonon coupling in spin nematics

Bapna, Monica

$NiGa_2 S_4$ is a spin-1 triangular magnet that may show spin-nematic ordering at low temperatures. From strong coupling expansion, it is seen that the effective Hamiltonian is a spin-1 bi-linear bi-quadratic model. The spin-phonon coupling modifies the coupling strengths in the effective Hamiltonian. As a manifestation of this magneto-elastic coupling, the relative change in sound speed would show a temperature dependence. We calculate the temperature dependence and study the associated Landau theory. This could be one of the experimental probes to test for the elusive ferro-nematic phase in the spin-1 triangular magnet.

### Exact diagonalization study of low-energy spectra and thermalization across a non-Fermi liquid to Fermi liquid transition

Bera, Surajit

We study non-equilibrium dynamics and many-body energy spectra near the ground state of a strongly interacting large-$N$ disordered fermionic model. The model is related to Sachdev-Ye-Kitaev (SYK) model and can be tuned to undergo a quantum phase transition (QPT) in the large-$N$ limit between a SYK non-Fermi liquid (NFL), having finite zero-temperature residual entropy, to a weakly interacting Fermi liquid phase (FL) with no residual entropy. We study many-body level spacing, single-particle spectral function, thermal entropy and entanglement properties of low-energy eigenstates across the NFL-FL transition beyond large-$N$ via numerical exact diagonalization. We also want to construct the effective low-energy field theory across the QPT by considering fluctuations around the large-$N$ limit. Furthermore, we explore out-of-equilibrium dynamics and thermalization after a quench across the QPT through time-evolution of entanglement entropy and non-equilibrium Green's functions.

### Charge carrier drop driven by spiral antiferromagnetism: a DMFT study

Bonetti, Pietro Maria

We compute properties of the spiral antiferromagnetic phase of the hole-doped two dimensional Hubbard model within the dynamical mean-field theory (DMFT). Using hopping parameters that fit real materials properties, we find a steep increase of the magnetic gap below the critical doping at which the order sets in. Hence, there is only a narrow doping region in which electron pockets are present, translating into a steep drop of the charge carrier density below the critical doping p∗.

### Planckian superconductor

Cheipesh, Yevheniia

The Planckian relaxation rate $\hbar/t_\mathrm{P} = 2\pi k_\mathrm{B} T$ sets a characteristic time scale for both equilibration of quantum critical systems and maximal quantum chaos. In this note, we show that at the critical coupling between a superconducting dot and the complex Sachdev-Ye-Kitaev model, known to be maximally chaotic, the pairing gap $\Delta$ behaves as $\eta \,\, \hbar/t_\mathrm{P}$ at low temperatures, where $\eta$ is an order one constant. Evanescence of the gap at $T=0$ and further coupling increase give rise to the lower critical temperature so that the finite $\Delta$ domain is sandwiched in between two critical temperatures.

### Phase diagram of a coupled luttinger liquid and its implications to the twisted bilayer graphene

Chen, Chuan

We explore in detail the electronic phases of a system consisting of three non-colinear arrays of coupled quantum wires, each rotated 120 degrees with respect to the next. A perturbative renormalization-group analysis reveals that multiple correlated states can be stabilized: a smectic or $d \pm id$ superconductor, a charge density wave insulator, a two-dimensional Fermi liquid, and a 2D Luttinger liquid (also known as smectic metal or sliding Luttingerliquid). The model provides an effective description of electronic interactions in small-angle twisted bilayer graphene and we discuss its implications in relation to the recent observation of correlated and superconducting ground states near commensurate densities, as well as the "strange metal" behaviour at finite temperatures as a natural outcome of the 2D Luttinger liquid phase.

### Exploring the Kondo Effect of an Extended Impurity with Chains of Co Adatoms in a Magnetic Field

Danu, Bimla

Motivated by recent STM experiments, we explore the magnetic field induced Kondo effect that takes place at symmetry protected level crossings in finite Co adatom chains. We argue that the effective two- level system realized at a level crossing acts as an extended impurity coupled to the conduction electrons of the substrate by a distribution of Kondo couplings at the sites of the chain. Using auxiliary-field quantum Monte Carlo simulations, which quantitatively reproduce the field dependence of the zero-bias signal, we show that a proper Kondo resonance is present at the sites where the effective Kondo coupling dominates. Our modeling and numerical simulations provide a theoretical basis for the interpretation of the STM spectrum in terms of level crossings of the Co adatom chains.

### Confinement of U(1) Dirac spin liquids by quenched disorder

Dey, Santanu

We consider the 2+1 dimensional compact qunatum electrodynamics QED 2+1 with 2N flavors of fermions as an effective theory of gapless fermionic U(1) spin liquids and analyze the interplay between the quenched randomness and magnetic monopoles arising in the model. If the microscopic lattice symmetries exclude the relevant monopole operators with smaller charges, the theory becomes essentially noncompact and non-confining. In this context, some authors have uncovered some finite disorder parametric regime of the non-compact theory where the spin-liquid phase is stable against random perturbations. In this paper we report that the most generic random perturbations to the theory drastically reduce the scaling dimension of even the higher charge monopole operators and therefore render the non-compact effective description incomplete. Consequently, we find that even for the cases where disorder remains marginal, confinement becomes unavoidable.

### Charge frustration and long range interactions in two-dimensional organic metals

Driscoll, Katherine

The charge-ordered, insulating state of the $\theta$-(ET)$_2$X organic salts undergoes a phase transition, or melting, to an unconventional metal. The latter displays persistent charge fluctuations, accompanied by very high resistivities above the Mott-Ioffe-Regel limit. Recent experiments have attributed the unusual charge dynamics observed to the frustration of charge ordering, caused by both the triangular lattice geometry and the presence of unscreened Coulomb interactions. Despite their experimental relevance and long history, relatively little is known theoretically about long range interactions on the lattice due to the limitations of available numerical methods. In order to understand the properties and melting of such a two-dimensional Wigner-Mott crystal, we have developed a new effective model which is motivated by previous studies of defect localization. In addition to the new effective model, we also present exact diagonalization results for the role of interaction range and charge frustration in zero temperature metal-insulator transitions for the square and the triangular lattices and discuss the importance of symmetry and boundary conditions in calculations of finite-sized systems.

### Mesoscopic phenomena in novel graphene-based structures

Gall, Vanessa

While literature on the influence of external fields on bilayer graphene without interactions and the influence of interactions on bilayer graphene without external fields exists, in reality one usually has to deal with both at the same time. While the presence of the external fields usually leads to shifts in the energy, in the case of bilayer graphene it also changes the momentum dependence from quadratic to quartic order in momentum. This band structure is what one needs as a starting point for any analytic perturbative treatment of interaction. Due to its valley and spin degree of freedom, which can both be influenced by external fields and interactions but in turn also change the influence of interaction in these system, one is ultimately left with a self-consistent problem that is not yet understood in the necessary detail. One example, where interaction effects are in fact not important, is the quantization of conductance in bilayer graphene quantum point contacts in perpendicular magnetic fields. Here one observes a curious transition from size quantization to Landau levels. Upon a closer look one can however observe the 0.7 structure, that disperses with in-plane magnetic field and is an interaction effect.

### Cluster Functional Renormalization Group approach to Quantum Spin Liquids

Gneist, Nico

The pseudofermion functional renormalization group (pf-FRG) is a semi-analytical method to discriminate for a given microscopic spin model whether the low-temperature states exhibit magnetic ordering or quantum spin liquid behavior emerge. However, the form of this quantum spin liquid cannot be inferred easily within this framework. We introduce a cluster pf-FRG approach to achieve a more stringent connection between a microscopic spin model and the emergent quantum spin liquid. To this purpose the lattice of the model is divided into several sublattice such that spatially structured fermion bilinear expectation values can be calculated on spatial clusters. This enables a criterion for positive identification of spin liquids with bilinear order parameters. As an application the $J_1-J_2$ SU($N$)-Heisenberg model on a square lattice is considered. In the large $N$ limit our method successfully captures the emergence of a $\pi$-flux spin liquid state at low temperatures. For N=2 we investigate the ground state in the strongly frustrated phase. Our results suggest that in this model no bilinear spin liquid emerges.

### Disorder driven multifractality transition in Weyl nodal loops

Gonçalves, Miguel

The robustness of certain material properties to perturbations is arguably the most appealing property of topological matter. Topological insulators stood out as an important class of topological materials [1,2] whose stability with respect to interactions and disorder is by now fairly well established [3,4]. Gapless systems can, however, also support non-trivial momentum-space topology and are expected to be less robust to such effects. Among these, are the Weyl nodal loop semimetals, for which the valence and conduction bands linearly touch along one-dimensional (1D) loops in the three-dimensional (3D) momentum space [5]. In this work, we study the effect of short-range disorder in Weyl nodal loop semimetals by numerically exact means. For arbitrary small disorder, a novel semimetallic phase is unveiled for which the momentum-space amplitude of the ground-state wavefunction is concentrated around the nodal line and follows a multifractal distribution. At a critical disorder strength, a semimetal to compressible metal transition occurs, coinciding with a multi- to single-fractality transition. The universality of this critical point is characterized by the correlation length and dynamical exponents. At considerably higher disorder, an Anderson metal-insulator transition is shown to take place. Our results show that the nature of the semimetallic phase in non-clean samples is fundamentally different from a clean nodal loop semimetal.

### Abelian Higgs model at four loops, fixed-point collision and deconfined criticality

Ihrig, Bernhard

The abelian Higgs model serves as a prime textbook example for the superconduction transition and the Anderson-Higgs mechanism. In fact, the n-component extension of the AH model was suggested as a relavant model to describe certain quantum phase transitions beyond the Landau-Ginzburg paradigm. Explicitly, in d=2+1 dimensions the case of n=2 was discussed lately due to its relation to the NCCP^1 model. In this context, recent numerical analyses argue in favor of a weakly first-order phase transition while there is also evidence for a continous transition. We study the AH model with n complex scalar fields at unprecedented four-loop order in the $4-\epsilon$ expansion and find that the annihilation of two fixed points occurs at a critical number of $n_c \approx 12.2 \pm 3.9$ in three dimensions. The nature of the emergent walking behavior just below the fixed point annihilation allows for so-called Miransky scaling and we comment on its possible implications for the deconfined quantum phase transition.

### Disorder and interactions in chiral wires: Life around the infinite randomness fixed point

Karcher, Jonas

We study the low-energy physics of a chain of Majorana fermions in the presence of interaction and disorder, emphasizing the difference between Majoranas and conventional (complex) fermions. While in the noninteracting limit both models are equivalent (in particular, belong to the same symmetry class BDI and flow towards the same infinite-randomness critical fixed point), their behavior differs drastically once interaction is added. Our density-matrix renormalization group calculations show that the complex-fermion chain remains at the noninteracting fixed point. On the other hand, the Majorana fermion chain experiences a spontaneous symmetry breaking and localizes for repulsive interaction. To explain the instability of the critical Majorana chain with respect to a combined effect of interaction and disorder, we consider interaction as perturbation to the infinite-randomness fixed point and calculate numerically two-wave-function correlation functions that enter interaction matrix elements. The numerical results supported by analytical arguments exhibit a rich structure of critical eigenstate correlations. This allows us to identify a relevant interaction operator that drives the Majorana chain away from the infinite-randomness fixed point. For the case of complex fermions, the interaction is irrelevant.

### Phonon attenuation in $\mathbb{Z}_2$ quantum spin liquids

Lang, Johannes

In $\mathbb{Z}_2$ quantum spin liquids low lying excitations in the form of visons can couple to lattice vibrations. The high degree of frustration in the spin lattice results in an enlarged unit cell for the visons, which in turn has a characteristic signature in phonon attenuation.

Lier, Ruben

TBD

### Quasiparticles as Detector of Topological Quantum Phase Transitions

Manna, Sourav

Phases and phase transitions provide an important framework to understand the physics of strongly correlated quantum many-body systems. Topologically ordered phases of matter are particularly challenging in this context, because they are characterized by long-range entanglement and go beyond the Landau-Ginzburg theory. A few tools have been developed to study topological phase transitions, but the needed computations are generally demanding, they typically require the system to have particular boundary conditions, and they often provide only partial information. There is hence a high demand for developing further probes. Here, we propose to use the study of quasiparticle properties to detect phase transitions. Topologically ordered states support anyonic quasiparticles with special braiding properties and fractional charge. Being able to generate a given type of anyons in a system is a direct method to detect the topology, and the approach is independent from the choice of boundary conditions. We provide three examples, and for all of them we find that it is sufficient to study the anyon charge to detect the phase transition point. This makes the method numerically cheap.

### An intermediate scale incoherent metal on the triangular lattice

Mendez-Valderrama, Juan Felipe

We study the onset of "bad" metallic behavior in a triangular lattice of spinless fermions with long-range interactions. To study the rich phenomenology of this model at intermediate temperatures, we work in the regime where the fermion hopping can be treated perturbatively in combination with a classical Monte Carlo simulation. With this approach, we describe the phase diagram of the system by calculating its electronic compressibility for a broad range of fillings and temperatures. Moreover, we characterize transport in the system by calculating its DC conductivity. For intermediate fillings close to the insulating transition, we observe a crossover between two linear-in-T regimes for the resistivity.

### Nuclear magnetic resonance in Weyl semimetals

Okvátovity, Zoltán

We focus on the hyperfine coupling and the NMR spin-lattice relaxation time, $T_1$ in Weyl semimetals. In these systems, the density of states varies with the square of the energy around the Weyl node. The naive power counting suggests a $1/T_1T\sim E^4$ scaling with $E$ the maximum of temperature ($T$) and chemical potential. By carefully investigating the hyperfine interaction between nuclear spins and Weyl fermions, we find that its spin part behaves conventionally, while its orbital part diverges unusually with the inverse of energy around the Weyl node. Consequently, the nuclear spin relaxation rate scales as $1/T_1T\sim E^2\ln(E/\omega_{\text{L}})$ with $\omega_{\text{L}}$ the nuclear Larmor frequency. We also analyze the experimental data on the spin-lattice relaxation rate of TaP crystal. The non-monotonic temperature dependence is explained by taking into account the temperature dependence of chemical potential. The anomalous behavior of $T_1$ allows us to introduce an effective hyperfine coupling constant, which is tunable by gating or doping.

### Quantization of orbital-Zeeman cross magnetic susceptibility in two-dimensional insulators

Ozaki, Soshun

There are three types of contributions to magnetism of Bloch electrons: orbital magnetism, Pauli paramagnetism, and the cross term of the two contributions, which we call here orbital-Zeeman cross term. Nakai and Nomura [1] pointed out that the orbital-Zeeman cross term is discretized and is proportional to the Chern number on the basis of phenomenological discussions and semi-classical calculations. Here we carry out microscopic calculations of magnetic susceptibility including orbital magnetism, Pauli paramagnetism, and orbital-Zeeman cross term in terms of thermal Green’s functions. For insulators at zero temperature, we see that there is a term of integral of the Berry curvature over the whole Brillouin zone, or the Chern number, which is consistent with the phenomenological discussion by Nakai and Nomura [1]. Next, we apply the new formula to a model for a topological insulator, silicene with Kane-Mele type spin-orbit interaction. It reflects the $Z_2$ topological invariant and is quantized with separation which does not depend on the detail of the model. [1]R. Nakai and K. Nomura, Phys. Rev. B 93, 214434 (2016).

### Jamming Dynamics in Hard-Core Spin Systems

Placke, Benedikt

Jamming is a phenomenon present in a wide range of physical systems ranging from granular materials and colloidal suspensions to foams and emulsions. A well studied toy model for such systems are hard spheres, which under compression undergo a jamming transition to an incompressible state at a critical packing fraction $\phi_c$ that is below the close packing fraction. Here, we study an analogously constrained model of spins on a lattice.

### A cascade of non-Fermi liquid crossovers from an interplay of local and bosonic quantum criticality

Schlief Raether, Andrés Felipe

I will present examples of multi-orbital electronic lattice models, coupled to bosonic collective modes with modified Sachdev-Ye-Kitaev form of interactions, which become solvable when the number of orbitals and collective modes is taken to be large. At high energies, these models display non-Fermi liquid behavior with local quantum criticality and are described by a strongly coupled electron-boson fluid. As a function of decreasing energy scales, they exhibit a crossover into an incipient heavy Fermi liquid regime, where the interaction between the bosonic mode and the coherent electronic quasiparticles near the Fermi surface leads to Landau damping. When the boson gap is tuned to criticality, the feedback of the damped boson on the electrons leads to a low-temperature non-Fermi liquid with a critical Fermi surface. Our models thus describe a cascade of crossovers from a dynamical critical exponent $z=\infty$ down to $z=3$ in a controlled setting as a function of decreasing energy scales.

### Spin-Phonon coupling in $Pr_2Zr_2O_7$ and possible experimental signatures

Seth, Arnab

It is well known that competing interactions due to geometric frustration in $Pr_2Zr_2O_7$ suppresses the conventional low-temperature symmetry broken magnetically ordered ground state in favour of long-range entangled quantum spin liquid states. The low energy manifold of this material captures both gapless photon like excitations and gapped magnetic monopole like excitations. Here we present a possible magnetoelastic coupling between the lattice degrees of freedom to those low energy excitations. Modified self-energy of the phonons due to this coupling and its low-temperature behaviour might be an extremely useful experimental signature for the spin liquid materials.

### Strain Modulation in a Chiral $p$-Wave Superconductor

Shibata, Yuto

I am sorry but I would like to submit the abstract of my poster presentation later. Could you let me know when the deadline for the submission is?

### Twisted Fracton Models in Three Dimensions

Song, Hao

We study novel three-dimensional gapped quantum phases of matter which support quasiparticles with restricted mobility, including immobile "fracton" excitations. So far, most existing fracton models may be instructively viewed as generalized Abelian lattice gauge theories. Here, by analogy with Dijkgraaf-Witten topological gauge theories, we discover a natural generalization of fracton models, obtained by twisting the gauge symmetries. Introducing generalized gauge transformation operators carrying an extra phase factor depending on local configurations, we construct a plethora of exactly solvable three-dimensional models, which we dub "twisted fracton models." A key result of our approach is to demonstrate the existence of rich non-Abelian fracton phases of distinct varieties in a three-dimensional system with finite-range interactions. For an accurate characterization of these novel phases, the notion of being inextricably non-Abelian is introduced for fractons and quasiparticles with one-dimensional mobility, referring to their new behavior of displaying braiding statistics that is, and remains, non-Abelian regardless of which quasiparticles with higher mobility are added to or removed from them. We also analyze these models by embedding them on a three-torus and computing their ground state degeneracies, which exhibit a surprising and novel dependence on the system size in the non-Abelian fracton phases. Moreover, as an important advance in the study of fracton order, we develop a general mathematical framework which systematically captures the fusion and braiding properties of fractons and other quasiparticles with restricted mobility.

### Parting the Fermi Sea at the Mott Point: Dynamics of Correlated Electrons Reveals the Mechanism Underpinning Mottness

Tan, Yuting

The fundamental nature of the Mott insulator-metal transition remains subject of controversy and debate. Early theories [1-3] favored a robust first-order scenario but it has proven difficult to identify conclusive experimental evidence for the expected phase-coexistence region [4-6] Alternative viewpoints envision a more continuous crossover at finite temperature featuring aspects of quantum criticality [7-10]. Recently, quantum spin liquids were recognized as the materials best suited for studying the pristine Mott state in absence of magnetic order [11] and its low-temperature transition to a Fermi liquid [10]. Our work demonstrate that dielectric permittivity represents the optimal quantity to distinguish the relevant physical regimes around the Mott point, in particular to reliably detect insulator-metal phase coexistence below the critical endpoint. By combining pressure-dependent dielectric spectroscopy with state-of-the-art theoretical modeling, we establish how the capacitive coupling between metallic puddles gives rise to a colossal peak in the permittivity reaching $\epsilon_1\approx 10^5$ within the coexistence region. Our results indicate that the observed inhomogeneities are the consequence of phase separation resulting from strong correlation effects inherent to Mottness. Ref: [1] N. F. Mott, Metal-Insulator Transitions, 2nd ed. (Taylor & Francis Ltd., Bristol, 1990). [2] A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg Rozenberg, Rev. Mod. Phys. 68, 13 (1996). [3] D. Vollhardt, Ann. Phys. (Berl.) 524, 1 (2012). [4] M. Imada, A. Fujimori, and Y. Tokura, Rev. Mod. Phys.70, 1039 (1998). [5] P. Limelette, A. Georges, D. Jerome, P. Wzietek, P. Metcalf, and J. M. Honig, Science 302, 89 (2003); F. Kagawa, T. Itou, K. Miyagawa, and K. Kanoda, Phys. Rev. B 69, 64511 (2004). [6] Y. Kurosaki, Y. Shimizu, K. Miyagawa, K. Kanoda, and G. Saito, Phys. Rev. Lett. 95, 177001 (2005). [7] T. Senthil, Phys. Rev. B 78, 45109 (2008). [8] J. Vucicevic, H. Terletska, D. Tanaskovic, and V. Dobrosavljevic, Phys. Rev. B 88, 75143 (2013). [9] T. Furukawa, K. Miyagawa, H. Taniguchi, R. Kato, and K. Kanoda, Nat. Phys. 11, 221 (2015). [10] T. Furukawa, K. Kobashi, Y. Kurosaki, K. Miyagawa, and K. Kanoda, Nat. Commun. 9, 307 (2018). [11] A. Pustogow, M. Bories, A. Lohle, R. Rosslhuber, E. Zhukova, B. Gorshunov, S. Tomic, J. A. Schlueter, R. Hubner, T. Hiramatsu, Y. Yoshida, G. Saito, R. Kato,T.-H. Lee, V. Dobrosavljevic, S. Fratini, and M. Dressel,Nat. Mater. 17, 773 (2018).

### Quantum Criticality of Semi-Dirac Fermions

Uryszek, Mikolaj

Two-dimensional semi-Dirac fermions are quasiparticles that disperse linearly in one direction and quadratically in the other. We investigate instabilities of semi-Dirac fermions toward charge and spin density wave and superconducting orders, driven by short-range interactions. We analyze the critical behavior of the Yukawa theories for the different order parameters using Wilson momentum shell renormalization group. We generalize to a large number of fermion flavors, N, to achieve analytic control in 2+1 dimensions and calculate critical exponents at one-loop order, systematically including universal 1/N corrections. The anomalous dimension of the fermion fields vanishes in the large N limit, consistent with a recovery of Fermi-liquid behaviour. However, many other unusual features persist. We show that this is a consequence of non-analytic terms in the mean-field free energy of semi-Dirac fermions.

### Gapless Coulomb State Emerging from a Self-Dual Topological Tensor-Network State

Zhu, Guo-Yi

In the tensor network representation, a deformed Z2 topological ground state wave function is proposed and its norm can be exactly mapped to the two-dimensional solvable Ashkin-Teller model. Then the topological (toric code) phase with anyonic excitations corresponds to the partial order phase of the Ashkin- Teller model, and possible topological phase transitions are precisely determined. With the electric- magnetic self-duality, a novel gapless Coulomb state with quasi-long-range order is obtained via a quantum Kosterlitz-Thouless phase transition. The corresponding ground state is a condensate of pairs of logarithmically confined electric charges and magnetic fluxes, and the scaling behavior of various anyon correlations can be exactly derived, revealing the effective interaction between anyons and their condensation. Deformations away from the self-duality drive the Coulomb state into either the gapped Higgs phase or the confining phase.

### Magnetic ordering induced by non-magnetic impurities in Sr$_2$RuO$_4$

Zinkl, Bastian

The experimental investigation of magnetic fluctuations in Ti-doped Sr$_2$RuO$_4$ has revealed strong, short ranged magnetic ordering at the incommensurate wave vector $\mathbf{q} \simeq (2 \pi /3, 2 \pi /3)$, which corresponds to the nesting vector of two out of three Fermi surface sheets. Motivated by these findings, we analyze the origin of magnetic ordering in a two-band system under the substitution of non-magnetic impurities. In detail, we examine the electromagnetic properties by combining a self-consistent Bogoliubov–de Gennes calculation with a phenomenological Ginzburg-Landau theory and an effective gauge field theory. Spontaneous spin currents and a finite spin polarization, dominated by the nesting vector, are induced around the impurities due to spin-orbit coupling and interorbital hybridization effects. Our findings illustrate how generic and intrinsic system properties lead to the formation of magnetic order in non-magnetically doped materials such as Sr$_{2}$Ru$_{1-x}$Ti$_{x}$O$_{4}$. In particular, we find that the available measurements are consistent with our theoretical predictions.