arXiv subjects

Guillermo R. Zemba

Publications and source records attributed to Guillermo R. Zemba.

At least 19 recordsLinked to original sources

arXiv2026

Fermi sea topology and boundary geometry for free particles in one- and two-dimensional lattices

Free gasses of spinless fermions moving on a lattice-symmetric geometric background are considered. Their topological properties at zero temperature can be used to classify their Fermi seas and associated boundaries. The flat orbifolds ${\Rb}^{d}/Γ$, where $Γ$ is the crystallographic group of symmetry in $d$-dimensional momentum space, are used to accomplish this task. Two topological classes exist for $d=1$: an interval, which is identified as a conductor, and a circumference, which corresponds to an insulator. The number of topological classes increases to 17 for $d=2$: 8 have the topology of a disk, that are generally recognized as conductors, and 4 correspond to a 2-sphere, matching insulators. Both sets eventually contain a finite number of conical singularities and reflection corners at the boundaries. The remaining cases in the listing relate to conductors (annulus, Möbius strip) and insulators (2-torus, real projective plane, Klein bottle). Examples that fall under this list are given, along with physical interpretations of the singularities. It is anticipated that the findings of this classification will be robust under perturbative interactions due to its topological character.

cond-mat.mes-hall↗

arXiv2025

Bosonic Bogoliubov transformations as Lorentz boosts in $(c,{\overline c})=(1,1)$ conformal field theories with marginal $J{\overline J }$ deformations

We consider conformal field theories with central charges $(c,{\overline c})=(1,1)$ that are invariant under the exchange of the holomorphic and antiholomorphic sectors, in both bosonic and fermionic realizations that are meaningful for condensed matter systems. The effect of marginal current-current $(J,{\overline J})$ perturbations is to induce a deformation of the Hilbert space given by a Lorentz boost in the 2D space of currents, which is identified with a Bogoliubov transformation. The rapidity of the boost is determined by the coupling constant of the marginal perturbation. When the perturbation is diagonal in the original currents of the theory, there is a linear relation between the two, and non-linear otherwise. In the fermionic cases, both free and with Calogero-Sutherland interactions, the marginal perturbation corresponds to backward scattering processes.

hep-th↗

arXiv2025

Quantum dynamics of the effective field theory of the Calogero-Sutherland model

We consider the known effective field theory of the Calogero-Sutherland model in the thermodynamic limit of large number of particles, obtained from the standard procedure in conformal field theory: the Hilbert space is constructed a priori in terms of irreducible representations of the symmetry algebra, and not by diagonalization of the hamiltonian, which is given in terms of fields that carry representations of the W-infinity algebra (representing the incompressibility of the Fermi sea). Nevertheless, the role of the effective hamiltonian of the theory is to establish a specific dynamics, which deserves further consideration. We show that the time evolution of the (chiral or antichiral) density field is given by the quantum Benjamin-Ono equation, in agreement with previous results obtained from the alternative description of the continuous limit of the model, based on quantum hydrodynamics. In this study, all calculations are performed at the quantum operator level, without making any assumption on the semiclassical limit of the fields and their equations of motion. This result may be considered as a reliable indication of the equivalence between the quantum field theoretic and quantum hydrodynamical formulations of the effective theories of the model. A one-dimensional quantum compressible fluid that includes both chiralities is the physical picture that emerges for the continuous limit of the Calogero-Sutherland model.

hep-th↗

arXiv2025

Dynamic structure factor of Calogero-Sutherland fluids

The effective extended conformal field theory with symmetry W_infinity*{bar W_infinity} that describes the thermodynamic limit of the Calogero-Sutherland model is considered. The dynamic structure factor of the chiral component in the repulsive regime is determined and compared with the corresponding one of the free bosonic theory, given that both share isomorphic Hilbert spaces but differ in the time evolution of quantum states. In either case, a sharp response function peaked at only one resonant frequency is found, and the physical implications of this outcome are addressed. Furthermore, a detailed comparison between this result and the corresponding one obtained in the first quantized formulation of the Calogero-Sutherland model is provided. Complete agreement in the parameter region in which both results overlap is found. This outcome provides further support to the equivalence between the first and second quantized treatments of the Calogero-Sutherland model, in which the computational advantages from integrability in the first formulation are paralleled by those from the algebraic structure of the second.

hep-th↗

arXiv2025

Effective short distance interaction in Calogero-Sutherland quantum fluids

We consider the effective conformal field theory with symmetry W-infinity x W-infinity that describes the thermodynamic limit of the Calogero-Sutherland model. In the repulsive regime of the free fermion formulation, we identify an attractive interaction between opposite moving particle-hole pairs that dominates the short distance behavior and that is proposed as responsible for the destabilization of the ground state, leading to a new one of bosonic nature. The process is described by a Bogoliubov transformation of the free fermion bilinear operators into bosonic ones, preserving the form of the W-infinity algebra but decoupling the opposite chirality terms in the hamiltonian, as expected in the low energy limit. In coordinate space this interaction has a short range component that arises due to the quantum regularization of the theory. The described dynamical process may be considered as a mechanism of the emergence of the known charge and quantum statistics fractionalization of the low lying excitations of the theory, as predicted in both first and second quantization studies.

hep-th↗

arXiv2024

Laminar flow of charged quantum fluids of the Calogero-Sutherland universality class

The effective field theory of the Calogero-Sutherland model represents a universality class of quantum hydrodynamic fluids in one spatial dimension. It describes quantum compressible fluids involving both chiralities in which the chiral density field obeys the quantum Benjamin-Ono equation. An extension of this theory to describe a laminar flow of the Calogero-Sutherland fluids in a rectangular geometry with small transverse width and the topology of a ribbon, is considered here. The physical picture is based on the edge states in the hierarchical quantum Hall effect, which may be seen as a collection of parallel one-dimensional quantum incompressible fluids moving along but confined within the transverse microscopic width of the edge of the sample. The effective theory is thus defined as the direct product of two one-dimensional theories of the Calogero-Sutherland class so that one involves motion while the other is confining. Charge transport may be induced by coupling the system to an external electromagnetic field that yields a global translation of the ground state. The effective theory describes quantum solitonic excitations along the direction of the flow and possesses a two-dimensional electric current density which shows a Wigner semicircle law profile in the transverse direction, suggesting a Poiseuille-like behavior but without dissipative viscous effects since the velocity of the fluid is not a well-defined quantum field. This simple physical picture predicts interesting phenomena with distinctive signatures that may be tested in real samples.

hep-th↗

arXiv2019

Universal power-law exponents in differential tunneling conductance for planar insulators near Mott criticality at low temperatures

We consider the low-temperature differential tunneling conductance $G$ for interfaces between a planar insulating material in the Mott-class and a metal. For values of the the applied potential difference $V$ that are not very small, there is a experimentally observed universal regime in which $G \sim V^m$, where $m$ is a universal exponent. We consider the theoretical prediction of the values of $m$ by using the method of Effective Field Theory ($EFT$), which is appropriate for discussing universal phenomena. We describe the Mott material by the $EFT$ pertaining the long-distance behavior of a spinless Hubbard-like model with nearest neighbors interactions previously considered. At the Mott transition, the $EFT$ is known to be given by a double Abelian Chern-Simons theory. The simplest realization of this theory at the tunneling interface yields a Conformal Field Theory with central charges $(c,\bar c) =(1,1)$ and Jain filling fraction $ν= 2/3$ describing a pair of independent counter-propagating chiral bosons (one charged and one neutral). Tunneling from the material into the metal is, therefore, described by this $EFT$ at the Mott critical point. The resulting tunneling conductance behaves as $G \sim V^{(1/ν-1)}$, yielding the prediction $m=1/2$, which compares well (within a $10 \%$ deviation) with the results for this exponent in two experimental studies considered here.

cond-mat.str-el↗

arXiv2015

Critical Theory of Two-Dimensional Mott Transition: Integrability and Hilbert Space Mapping

We reconsider the Mott transition in the context of a two-dimensional fermion model with density-density coupling. We exhibit a Hilbert space mapping between the original model and the Double Lattice Chern-Simons theory at the critical point by use of the representation theory of the q-oscillator and Weyl algebras. The transition is further characterized by the ground state modification. The explicit mapping provides a new tool to further probe and test the detailed physical properties of the fermionic lattice model considered here and to enhance our understanding of the Mott transition(s).

cond-mat.str-el↗

arXiv2010

Effective Field Theory and Integrability in Two-Dimensional Mott Transition

We study the Mott transition in a two-dimensional lattice spinless fermion model with nearest neighbors density-density interactions. By means of a two-dimensional Jordan-Wigner transformation, the model is mapped onto the lattice XXZ spin model, which is shown to possess a Quantum Group symmetry as a consequence of a recently found solution of the Zamolodchikov Tetrahedron Equation. A projection (from three to two space-time dimensions) property of the solution is used to identify the symmetry of the model at the Mott critical point as U_q(sl(2))xU_q(sl(2)), with deformation parameter q=-1. Based on this result, the low-energy Effective Field theory for the model is obtained and shown to be a lattice double Chern-Simons theory with coupling constant k=1 (with the standard normalization). By further employing the Effective Filed Theory methods, we show that the Mott transition that arises is of topological nature, with vortices in an antiferromagnetic array and matter currents characterized by a d-density wave order parameter. We also analyze the behavior of the system upon weak coupling, and conclude that it undergoes a quantum gas-liquid transition which belongs to the Ising universality class.

cond-mat.str-el↗

arXiv2009

Coulomb Blockade in Hierarchical Quantum Hall Droplets

The degeneracy of energy levels in a quantum dot of Hall fluid, leading to conductance peaks, can be readily derived from the partition functions of conformal field theory. Their complete expressions can be found for Hall states with both Abelian and non-Abelian statistics, upon adapting known results for the annulus geometry. We analyze the Abelian states with hierarchical filling fractions, ν=m/(mp \pm 1), and find a non trivial pattern of conductance peaks. In particular, each one of them occurs with a characteristic multiplicity, that is due to the extended symmetry of the m-folded edge. Experimental tests of the multiplicity can shed more light on the dynamics of this composite edge.

cond-mat.mes-hall↗

arXiv2009

Topological phase transition in a RNA model in the de Gennes regime

We study a simplified model of the RNA molecule proposed by G. Vernizzi, H. Orland and A. Zee in the regime of strong concentration of positive ions in solution. The model considers a flexible chain of equal bases that can pairwise interact with any other one along the chain, while preserving the property of saturation of the interactions. In the regime considered, we observe the emergence of a critical temperature T_c separating two phases that can be characterized by the topology of the predominant configurations: in the large temperature regime, the dominant configurations of the molecule have very large genera (of the order of the size of the molecule), corresponding to a complex topology, whereas in the opposite regime of low temperatures, the dominant configurations are simple and have the topology of a sphere. We determine that this topological phase transition is of first order and provide an analytic expression for T_c. The regime studied for this model exhibits analogies with that for the dense polymer systems studied by de Gennes

q-bio.BM↗

arXiv2008

Mott transition and integrable lattice models in two dimensions

We describe the two-dimensional Mott transition in a Hubbard-like model with nearest neighbors interactions based on a recent solution to the Zamolodchikov tetrahedron equation, which extends the notion of integrability to two-dimensional lattice systems. At the Mott transition, we find that the system is in a d-density wave or staggered flux phase that can be described by a double Chern Simons effective theory with symmetry \su2 \otimes \su2. The Mott transition is of topological nature, characterized by the emergence of vortices in antiferromagnetic arrays interacting strongly with the electric charges and an electric-magnetic duality. We also consider the effect of small doping on this theory and show that it leads to a quantum gas-liquid coexistence phase, which belongs to the Ising universality class and which is consistent with several experimental observations.

cond-mat.str-el↗

arXiv2008

Thermodynamics of a model for RNA folding

We analyze the thermodynamic properties of a simplified model for folded RNA molecules recently studied by G. Vernizzi, H. Orland, A. Zee (in {\it Phys. Rev. Lett.} {\bf 94} (2005) 168103). The model consists of a chain of one-flavor base molecules with a flexible backbone and all possible pairing interactions equally allowed. The spatial pseudoknot structure of the model can be efficiently studied by introducing a $N \times N$ hermitian random matrix model at each chain site, and associating Feynman diagrams of these models to spatial configurations of the molecules. We obtain an exact expression for the topological expansion of the partition function of the system. We calculate exact and asymptotic expressions for the free energy, specific heat, entanglement and chemical potential and study their behavior as a function of temperature. Our results are consistent with the interpretation of $1/N$ as being a measure of the concentration of $\rm{Mg}^{++}$ in solution.

q-bio.BM↗

arXiv2008

Effective Field Theories for Electrons in Crystalline Structures

We present an effective field theory formulation for a class of condensed matter systems with crystalline structures for which some of the discrete symmetries of the underlying crystal survive the long distance limit, up to mesoscopic scales, and argue that this class includes interesting materials, such as $Si$-doped $GaAs$. The surviving symmetries determine a limited set of possible effective interactions, that we analyze in detail for the case of $Si$-doped $GaAs$ materials. These coincide with the ones proposed in the literature to describe the spin relaxation times for the $Si$-doped $Ga As$ materials, obtained here as a consequence of the choice of effective fields and their symmetries. The resulting low-energy effective theory is described in terms of three (six chiral) one-dimensional Luttinger liquid systems and their corresponding intervalley transitions. We also discuss the Mott transition within the context of the effective theory.

cond-mat.mes-hall↗

arXiv2002

A new class of Matrix Models arising from the W-infinity Algebra

We present a new class of hermitian one-matrix models originated in the W-infinity algebra: more precisely, the polynomials defining the W-infinity generators in their fermionic bilinear form are shown to expand the orthogonal basis of a class of random hermitian matrix models. The corresponding potentials are given, and the thermodynamic limit interpreted in terms of a simple plasma picture. The new matrix models can be successfully applied to the full bosonization of interesting one-dimensional systems, including all the perturbative orders in the inverse size of the system. As a simple application, we present the all-order bosonization of the free fermionic field on the one-dimensional lattice.

hep-th↗

arXiv2001

Thermal Transport in Chiral Conformal Theories and Hierarchical Quantum Hall States

Chiral conformal field theories are characterized by a ground-state current at finite temperature, that could be observed, e.g. in the edge excitations of the quantum Hall effect. We show that the corresponding thermal conductance is directly proportional to the gravitational anomaly of the conformal theory, upon extending the well-known relation between specific heat and conformal anomaly. The thermal current could signal the elusive neutral edge modes that are expected in the hierarchical Hall states. We then compute the thermal conductance for the Abelian multi-component theory and the W-infinity minimal model, two conformal theories that are good candidates for describing the hierarchical states. Their conductances agree to leading order but differ in the first, universal finite-size correction, that could be used as a selective experimental signature.

cond-mat.mes-hall↗

arXiv1998

Hamiltonian Formulation of the W-Infinity Minimal Models

The W-infinity minimal models are conformal field theories which can describe the edge excitations of the hierarchical plateaus in the quantum Hall effect. In this paper, these models are described in very explicit terms by using a bosonic Fock space with constraints, or, equivalently, with a non-trivial Hamiltonian. The Fock space is that of the multi-component Abelian conformal theories, which provide another possible description of the hierarchical plateaus; in this space, the minimal models are shown to correspond to the sub-set of states which satisfy the constraints. This reduction of degrees of freedom can also be implemented by adding a relevant interaction to the Hamiltonian, leading to a renormalization-group flow between the two theories. Next, a physical interpretation of the constraints is obtained by representing the quantum incompressible Hall fluids as generalized Fermi seas. Finally, the non-Abelian statistics of the quasi-particles in the W-infinity minimal models is described by computing their correlation functions in the Coulomb Gas approach.

hep-th↗

arXiv1996

W-infinity Field Theories for the Edge Excitations in the Quantum Hall Effect

We briefly review these low-energy effective theories for the quantum Hall effect, with emphasis and language familiar to field theorists. Two models have been proposed for describing the most stable Hall plateaus (the Jain series): the multi-component Abelian theories and the minimal W-infinity models. They both lead to a-priori classifications of quantum Hall universality classes. Some experiments already confirmed the basic predictions common to both effective theories, while other experiments will soon pin down their detailed properties and differences. Based on the study of partition functions, we show that the Abelian theories are rational conformal field theories while the minimal W-infinity models are not.

hep-th↗