Luttinger Liquids and Non-Fermi Liquid States in one dimension pdf file Non-Fermi liquids: Luttinger liquids in one-dimensional and quasi-one-dimensional systems: quantum wires, carbon nano-tubes and quantum Hall edges. Abelian bosonization. Non-perturbative theory of interacting fermi systems in one dimension. Luttinger liquids.
Application to the Kondo problem and other quantum impurity systems. Luttinger physics and its connecions with the quantum Hall effect, and quantum impurity problems. Tunneling into non-Fermi liquids. Extensions to higher dimensions and the stability of The Landau theory. Disorder, Diffusion and Localization , scanned notes The role of disorder in weakly interacting Fermi systems. The Born approximation. Multiple scattering. The elastic mean free path. Quantum diffusion and Boltzmann conductivity.
Ladder diagrams. The Ioffe-Regel criterion. Anderson localization in strongly disordered non-interacting systems. Lifshitz tails. The localization length. The metal-insulator transitions. The Thouless length. Almost Absence of diffusion in two dimensions and scaling theories of weak localization. Non-linear sigma models and replicas. Quantum Impurities in metals, the Anderson and Kondo Problems theory of a single magnetic impurity in a Fermi liquid. The Kondo effect. Reduction to a one-dimensional problem. Perturbation theory and Poor Man's Scaling.
The BCS Instability. Cooper pairs. The BCS wavefunction. Superconductors and Superfluids. Landau-Ginzburg theory. Electromagnetic Response and the Meissner effect. The Josephson effect and macroscopic quantum coherence. Anisotropic superconductivity: He3 and High temperature Superconductors. Stoner ferromagnetism. Spin and Charge Density Waves. The Hubbard Model at half-filling. Mott insulators. The strong coupling limit of the Hubbard model and the quantum Heisenberg model.
Spin-wave approximation and antiferromagnetism.
Phase transitions in magnets at finite temperature. Mean field theory. Critical phenomena. Scaling and the Renormalization Group. One-dimensional Quantum Antiferromagnets. Critical behavior. The role of spin. Quantum disordered states and Haldane gaps. The Sigma Model picture of antiferromagnets in one and two dimensions. Quantum critical behavior. Brief review of the renormalization group. Solitons and their quantum numbers. Quantum phase transitions. The integer quantum Hall effect. Quantization of the Hall conductance. Chern numbers and adiabatic topological invariants.
Disorder and correlations. The Fractional quantum Hall effects. The Laughlin wave function s. Quasiparticles and quasiholes. Fractional charge and fractional statistics. Effective hydrodynamic theories of the quantum Hall effects. The role of topology. Flux attachment. Composite bosons and composite fermions.
Paired FQH states. Inhomogeneous and compressible quantum Hall states. Doped Mott Insulators Quantum and classical phase separation: correlations and fluctuations. Stripe phases and electronic liquid crystal states. Non-Fermi liquid behavior. Connections with mechanisms of high temperature superconductivity. Spin liquids, and other exotic beasts. Quantum disordered states in strongly correlated systems.
Frustrated quantum antiferromagnets. Phases of frustrated quantum antiferromagnets. Spin liquids and liquid crystal phases. Gauge theory approaches to Strongly Correlated Systems.
SciPost Submission: Diffusion in generalized hydrodynamic
When are these states physical? Quantum Dimer Models. Confinement and deconfinement of excitations. Spin-Charge separation: when, where and why. However the definition and detection of such properties in a non-equilibrium setting is non-trivial. We employ the perspective of the entanglement spectrum, a generalization of entanglement entropy.
We show that it is well suited to the analysis of non-equilibrium states by applying it to i define topological invariants in Floquet Chern Insulators and ii extract universal exponents in critical prethermalization states. Abstract : In Weyl materials the valence and conduction electron bands touch at an even number of isolated points in the Brillouin zone. In the vicinity of these points the electron dispersion is linear and may be described by the massless Dirac equation.
This results in nontrivial topology of the Berry connection curvature. One of its consequences is the existence of peculiar surface electron states whose Fermi surfaces form arcs connecting projections of the Weyl points onto the surface plane. Band bending near the boundary of the crystal also produces surface states.
We show that in Weyl materials band bending near the crystal surface gives rise to a spiral structure of energy surfaces of arc states. The corresponding Fermi surface has the shape of a spiral that winds about the projection of the Weyl point onto the surface plane. The direction of the winding is determined by the helicity of the Weyl point and the sign of the band-bending potential. For close valleys the arc state morphology may be understood in terms of the avoided crossing of oppositely winding spirals.
Abstract: We study disordered topological crystalline phases for which the disorder is exactly symmetric under a given spatial symmetry operation.
Quasiparticle engineering and entanglement propagation
This requires that we go beyond the conventional momentum-space description of topological crystalline phases. Instead, we provide an understanding of the topology of the ground state in real-space. To do this, we discuss a mechanism wherein the topological invariant of the ground state is carried by bulk states which are localized within spatial regions that remain invariant under the relevant spatial symmetry. We illustrate our results with specific realizations of mirror-symmetric DIII topological superconductors in two and three spatial dimensions. Finally, we comment on how these results can provide a bulk characterization of disordered topological crystalline phases protected by average symmetries.
It is of interest in diverse fields such as the physics of 3He, quantum Hall physics, unconventional superconductivity and topological quantum computing. It naturally incorporates the parity and time reversal violating effects such as the Hall viscosity and the edge current. In addition, I will also describe the few-body aspects of this problem and introduce the super Efimov effect- a new type of three-body quantum universality manifesting itself in a tower of three-body bound states with a double-exponential scaling.
Here, we show that switching current measurements provide accessible and robust signatures for topological superconductivity which persist in the presence of quasiparticle poisoning processes. Such measurements provide access to the phase-dependent subgap spectrum and Josephson currents of the topological junction when incorporating it into an asymmetric SQUID together with a conventional Josephson junction with large critical current. We also argue that pump-probe experiments with multiple current pulses provide access to the quasiparticle poisoning rates of the topological junction.
The proposed signatures are particularly robust, even in the presence of Zeeman fields and spin-orbit coupling, when focusing on short Josephson junctions. Finally, we also consider microwave excitations of short topological Josephson junctions which may complement switching current measurements. Abstract : We investigate the phase diagram of a quantum spin-1 chain whose Hamiltonian is invariant under a global onsite A4, translation and lattice inversion symmetries. We detect different gapped phases characterized by SPT order and symmetry breaking using matrix product state order parameters.
We observe a rich variety of phases of matter characterized by a combination of symmetry breaking and symmetry fractionalization and also the interplay between the onsite and spatial symmetries. Examples of continuous phase transitions directly between topologically nontrivial SPT phases are also observed. Title : Topological order, symmetry, and Hall response of two-dimensional spin-singlet superconductors. Abstract : Fully gapped two-dimensional superconductors coupled to dynamical electromagnetism are known to exhibit topological order.
These theories capture the quantum statistics and fusion rules of low-energy excitations and incorporate global continuous symmetries - specifically, spin rotation and conservation of magnetic flux - present in all singlet superconductors. We compute the Hall response for these symmetries and investigate the physics at the edge. Abstract : We present a dimensional reduction argument to derive the classification reduction of fermionic symmetry protected topological phases in the presence of interactions.
The dimensional reduction proceeds by relating the topological character of a d-dimensional system to the number of zero-energy bound states localized at zero-dimensional topological defects present at its surface. This correspondence leads to a general condition for symmetry preserving interactions that render the system topologically trivial, and allows us to explicitly write a quartic interaction to this end.
Our reduction shows that all phases with topological invariant smaller than n are topologically distinct, thereby reducing the non-interacting Z classification to Zn. Abstract : Quantum corrections to charge transport can give rise to an oscillatory magnetoconductance, typically observed in mesoscopic samples with a length shorter than or comparable with the phase coherence length. Abstract : Recently, nanoscale pn-junction rings have been introduced as a vehicle for confinement of electronic states in Dirac materials . Confined states in these Dirac quantum dots arise due to constructive interference of electronic waves incident at the pn junction at oblique angles and inward-reflected from the ring.
What special features sets Dirac quantum dots apart from conventional quantum dots? We show  that Berry curvature induces a strongly non-reciprocal spectrum of quantum dot resonances under weak magnetic fields. Such effect is maximal for massless Dirac electrons, e. This non-reciprocity effect overwhelms the conventional orbital and spin-induced non-reciprocity.
The predicted giant non-reciprocity is readily accessible by Faraday and Kerr optical rotation measurements as well as by scanning tunneling spectroscopy. Abstract : The search for truly quantum phases of matter is one of the center pieces of modern research in condensed matter physics. Quantum spin liquids are exemplars of such phases. In the quest for the latter, the challenges are many: neither is it clear how to look for nor how to describe them, and definitive experimental examples of quantum spin liquids are still missing.
The phase diagram also contains an interacting bosonic topological insulator phase. Crucially, this model is expected to describe actual materials, and I provide a detailed set of material-specific constraints which may be readily used for an experimental realization. Abstract : We study Weyl semimetals in the presence of generic disorder, consisting of a random vector potential as well as a random scalar potential.
We derive renormalization group flow equations to second order in the disorder strength. These flow equations predict a disorder-induced phase transition between a pseudo-ballistic weak-disorder phase and a diffusive strong-disorder phase for sufficiently strong random scalar potential or for a pure three-component random vector potential.
We verify these predictions using a numerical study of the density of states near the Weyl point and of quantum transport properties at the Weyl point. In contrast, for a pure single-component random vector potential we find no transition to a diffusive strong-disorder phase. Title : Non-Anderson disorder-driven transitions in Weyl semimetals and other systems. In contrast to the conventional wisdom, it manifests itself in, e. The transition can be observed in Weyl semimetals, chiral superconductors, arrays of ultracold ions with long-range interactions, and other systems.
Abstract : A magnetic skyrmion is a vortex-like spin texture, which is characterized by a topological number. We theoretically study the quantum effects on magnetic skyrmions in two-dimensional chiral magnets. We also show that the critical behavior between the quantum liquid phase and the ferromagnetic phase depends on the spin size S and the topological number of a single skyrmion. In particular, for two adjacent non-contractible regions on a tripartite torus, the entanglement negativity provides a simple way to distinguish Abelian and non-Abelian theories.
Our results agree with the edge theory approach in a recent work X. Wen, S. Matsuura and S. Ryu, arXiv Abstract : On the triangular and kagome lattices, short-ranged resonating valence bond RVB wave functions can be sampled without the sign problem using a recently-developed Pfaffian Monte Carlo scheme . In this poster , we present a study of the Renyi entanglement entropy in these wave functions using a replica-trick method .
We prove that the mutual statistics are consistent with the toric code anyon model and rule out any other quasiparticle statistics such as the double semion model. Abstract : Out-of-equilibrium systems can host phenomena that transcend the usual restrictions of equilibrium systems. Here we unveil how out-of-equilibrium states, prepared via a quantum quench, can exhibit a non-zero Hall-type response that persists at long times, and even when the instantaneous Hamiltonian is time reversal symmetric; both these features starkly contrast with equilibrium Hall currents.
Interestingly, the persistent Hall effect arises from processes beyond those captured by linear response, and is a signature of the novel dynamics in out-of-equilibrium systems. We propose quenches in two-band Dirac systems as natural venues to realize persistent Hall currents, which exist when either mirror or time-reversal symmetry are broken before or after the quench. Its long time persistence, as well as sensitivity to symmetry breaking, allow it to be used as a sensitive diagnostic of the complex out-equilibrium dynamics readily controlled and probed in cold-atomic optical lattice experiments.
Abstract : The ferromagnetic kagome lattice is theoretically known to possess topological electronic  and magnonic  band structures. Previous polycrystal studies on Fe3Sn2, a ferromagnetic metal with underlying bi-layer kagome lattice, have shown unconventional magnetic and transport properties [3,4]. Here we present a first systematic magnetic and transport investigation on single crystalline Fe3Sn2.
We identified a spin-reorientation transition with temperature from anisotropic magnetic susceptibility. Furthermore, the anomalous Hall conductivity in single crystalline Fe3Sn2 is found to be at the crossover between intrinsic regime and clean limit in the universal anomalous Hall effect classification .
Title : Stripe melting, a transition between weak and strong symmetry protected topological phases. Abstract : In this poster, we construct a phase transition between weak and strong SPT phase in strongly interacting boson system. We find that the boundary is thermalized and investigate how its boundary anomaly, dictated by the bulk SPT order, is encoded in the quantum chaotic eigenspectrum of the SYK model. We show that given the SPT symmetry class, the boundary many-body level statistics varies among those of the three different Wigner-Dyson random matrix ensembles with a periodicity in the index that matches the interaction-reduced classification of the bulk SPT states.
Title : Spectral narrowing and spin echo for localized carriers with heavy-tailed Levy distribution of hopping times. Abstract : We study analytically the free induction decay and the spin echo decay originating from the localized carriers moving between the sites which host random magnetic fields. In the latter domain the decay does not follow a simple-exponent law.
To capture the behavior of the average spin in this domain, we solve the evolution equation for the average spin using the approach different from the conventional approach based on the Laplace transform. Unlike the free induction decay, the tail in the distribution of the residence times leads to the slow decay of the spin echo. The echo is dominated by realizations of the carrier motion for which the number of sites, visited by the carrier, is minimal. Abstract : Topological entanglement entropy has been regarded as a smoking-gun signature of topological order in two dimensions, capturing the total quantum dimension of the topological particle content.
An extrapolation method on cylinders has been used frequently to measure the topological entanglement entropy. We propose a simple numerical procedure to measure the replica correlation length through replica correlation functions. We also calculate the replica correlation functions for representative wave functions of abelian discrete gauge theories and the double semion theory in 2D, to show that they decay abruptly to zero. This supports a conjecture that the replica correlation length being small implies that the subleading term from the extrapolation method determines the total quantum dimension.
Skip to main content. Victor Albert Yale University Title : Geometrical, response, and gap properties of Lindbladians Abstract : Markovian reservoir engineering, in which time evolution of a quantum system is governed by a Lindblad master equation, is a powerful tool in studies of quantum matter and quantum information processing.
Anffany Chen University of British Columbia Title : Superconducting proximity effect and Majorana flat bands in the surface of a Weyl semimetal Abstract : We study the proximity effect between an s-wave superconductor SC and the surface states of a Weyl semimetal. Soonwon Choi Harvard University Title : Dissipative preparation of AKLT ground states in atomic arrays Abstract : The ground states of the Affleck-Lieb-Kennedy-Tasaki AKLT Hamiltonian are exactly solvable and have played an important role in understanding various concepts such as valence bond solid order, symmetry protected topological order, and matrix product states.
Luca Delacretaz Stanford Title : Memory matrix theory of quantum fluctuating superconductivity based on arxiv. Dominic V. Top Session 2 Yi-Ting Hsu Cornell University Title : Topological superconductivity in monolayer transition metal dichalcogenides Abstract : Theoretically it has been long known that breaking spin-degeneracy to realize so-called spinless fermions is a promising path to topological superconductivity.
Shenghan Jiang Boston College Title : Symmetric tensor networks — algorithms to sharply identify classes of quantum phases distinguishable by short-range physics Abstract : Phases of matter are sharply defined in the thermodynamic limit.
Byungmin Kang University of California, Berkeley Title : Universal crossover from ground state to excited-state quantum criticality Abstract : We study the non-equilibrium properties of a non-ergodic random quantum chain in which highly excited eigenstates exhibit critical properties usually associated with quantum critical ground states. Jack Kemp University of Oxford Title : Existence of strong edge zero modes in interacting, non-integrable systems Abstract : Strong edge zero modes are operators localised at the edge of a one-dimensional system which commute with the Hamiltonian, leading to a degeneracy in the entire energy spectrum.
Thomas Kvorning Stockholm University Title : Geometric effects of chiral superconductors Abstract : For conventional s-wave superconductors the order parameter has no directionality and therefore no magnetic response to geometry. Hughes Abstract: We study disordered topological crystalline phases for which the disorder is exactly symmetric under a given spatial symmetry operation.
Abhishodh Prakash Stony Brook University Title : Detection of gapped 1D phases with on-site and spatial symmetries Abstract : We investigate the phase diagram of a quantum spin-1 chain whose Hamiltonian is invariant under a global onsite A4, translation and lattice inversion symmetries. Abhiav Prem University of Colorado, Boulder Title : Topological order, symmetry, and Hall response of two-dimensional spin-singlet superconductors Abstract : Fully gapped two-dimensional superconductors coupled to dynamical electromagnetism are known to exhibit topological order.
Raquel Queiroz Max Planck Institute for Solid State Physics Title : Dimensional hierarchy of fermionic interacting topological phases Abstract : We present a dimensional reduction argument to derive the classification reduction of fermionic symmetry protected topological phases in the presence of interactions.
Top Session 3 Willem Rischau Ecole superieure de physique et chimie industrielles ESPCI Title : Quantum interference detected in a macroscopic Van der Waals conductor Abstract : Quantum corrections to charge transport can give rise to an oscillatory magnetoconductance, typically observed in mesoscopic samples with a length shorter than or comparable with the phase coherence length. Levitov, arXiv Bjoern Sbierski FU Berlin Title : Weyl node with random vector potential Abstract : We study Weyl semimetals in the presence of generic disorder, consisting of a random vector potential as well as a random scalar potential.
Wildeboer and A. Wildeboer, A. Seidel, and R. Melko, submitted to PRL. Hastings, I.
Correlation Functions and Quasiparticle Interactions in Condensed Matter
Gonzalez, A. Kallin, and R. Justin Wilson Caltech Title : Persistent Hall response in a quantum quench Abstract : Out-of-equilibrium systems can host phenomena that transcend the usual restrictions of equilibrium systems. Phys : Cond. Phys: Cond. Yue Zhang University of Utah Title : Spectral narrowing and spin echo for localized carriers with heavy-tailed Levy distribution of hopping times Abstract : We study analytically the free induction decay and the spin echo decay originating from the localized carriers moving between the sites which host random magnetic fields.
Liujun Zou MIT Title : Spurious Long-Range Entanglement and Replica Correlation Length Abstract : Topological entanglement entropy has been regarded as a smoking-gun signature of topological order in two dimensions, capturing the total quantum dimension of the topological particle content. Session 1.