
Santos, R., Gutman, D. and Carr, S. (2019). Interplay between intrinsic and emergent topological protection on interacting helical modes. Physical Review B: Condensed Matter and Materials Physics [Online] 99:75129. Available at: https://doi.org/10.1103/PhysRevB.99.075129.
The interplay between topology and interactions on the edge of a twodimensional topological insulator with timereversal symmetry is studied. We consider a simple noninteracting system of three helical channels with an inherent
Z_2 topological protection and hence a zerotemperature conductance of G=e^2/h. We show that when interactions are added to the model, the ground state exhibits two different phases as a function of the interaction parameters. One of these phases is a trivial insulator at zero temperature, as the symmetry protecting the noninteracting topological phase is spontaneously broken. In this phase there is zero conductance (G=0) at zero temperature. The other phase displays enhanced topological properties, with a topologically protected zerotemperature conductance of G=3e^2/h and an emergent Z_3 symmetry not present in the lattice model. The neutral sector in this phase is described by a massive version of Z_3
parafermions. This state is an example of a dynamically enhanced symmetryprotected topological state.

Camacho, G., Schmitteckert, P. and Carr, S. (2019). Exact equilibrium results in the interacting resonant level model. Physical Review B: Condensed Matter and Materials Physics [Online] 99:85122. Available at: https://doi.org/10.1103/PhysRevB.99.085122.
We present exact results for the susceptibility of the interacting resonant level model in equilibrium. Detailed simulations using both the numerical renormalization group and density matrix renormalization group were performed in order to compare with closed analytical expressions. By first bosonizing the model and then utilizing the integrability of the resulting boundary sineGordon model, one finds an analytic expression for the relevant energy scale T_K with excellent agreement to the numerical results. On the other hand, direct application of the Bethe ansatz of the interacting resonant level mode does not correctly reproduce T_K —however, if the bare parameters in the model are renormalized, then quantities obtained via the direct Bethe ansatz such as the occupation of the resonant level as a function of the local chemical potential do match the numerical results. The case of one lead is studied in the most detail, with many results also extending to multiple leads, although there still remain open questions in this case.

Kainaris, N., Carr, S. and Mirlin, A. (2018). Transmission through a potential barrier in Luttinger liquids with a topological spin gap. Physical Review B [Online] 97:115107. Available at: https://doi.org/10.1103/PhysRevB.97.115107.
We study theoretically the transport of the onedimensional singlechannel interacting electron gas through a strong potential barrier in the parameter regime where the spin sector of the lowenergy theory is gapped by interaction (LutherEmery liquid). There are two distinct phases of this nature, of which one is of particular interest as it exhibits nontrivial interactioninduced topological properties. Focusing on this phase and using bosonization and an expansion in the tunneling strength we calculate the conductance through the barrier as a function of the temperature as well as the local density of states (LDOS) at the barrier. Our main result concerns the mechanism of boundstatemediated tunneling. The characteristic feature of the topological phase is the emergence of protected zeroenergy bound states with fractional spin located at the impurity position. By flipping this fractional spin, single electrons can tunnel across the impurity even though the bulk spectrum for spin excitations is gapped. This results in a finite LDOS below the bulk gap and in a nonmonotonic behavior of the conductance. The system represents an important physical example of an interacting symmetryprotected topological phase, which combines features of a topological spin insulator and a topological charge metal, in which the topology can be probed by measuring transport properties.

Kainaris, N., Santos, R., Gutman, D. and Carr, S. (2017). Interaction induced topological protection in onedimensional conductors. Fortschritte der Physik [Online] 65:1600054. Available at: https://doi.org/10.1002/prop.201600054.
We discuss two one?dimensional model systems – the first is a single channel quantum wire with Ising anisotropy, while the second is two coupled helical edge states. We show that the two models are governed by the same low energy effective field theory, and interactions drive both systems to exhibit phases which are metallic, but with all single particle excitations gapped. We show that such states may be either topological or trivial; in the former case, the system demonstrates gapless end states, and insensitivity to disorder.

Carr, S., Santos, R. and Gutman, D. (2016). Phase diagram of two interacting helical states. Physical Review B: Condensed Matter and Materials Physics [Online] 93. Available at: http://dx.doi.org/10.1103/PhysRevB.93.235436.
We consider two coupled timereversalinvariant helical edge modes of the same helicity, such as would occur on two stacked quantum spin Hall insulators. In the presence of interaction, the lowenergy physics is described by two collective modes, one corresponding to the total current flowing around the edge and the other one describing relative fluctuations between the two edges.We find that quite generically, the relative mode becomes gapped at low temperatures, but only when tunneling between the two helical modes is nonzero. There are two distinct possibilities for the gapped state depending on the relative size of different interactions. If the intraedge interaction is stronger than the interedge interaction, the state is characterized as a spinnematic phase. However,
in the opposite limit, when the interaction between the helical edge modes is strong compared to the interaction within each mode, a spindensity wave forms, with emergent topological properties. First, the gap protects the conducting phase against localization by weak nonmagnetic impurities; second, the protected phase hosts localized zero modes on the ends of the edge that may be created by sufficiently strong nonmagnetic impurities.

Kainaris, N. and Carr, S. (2015). Emergent topological properties in interacting onedimensional systems with spinorbit coupling. PHYSICAL REVIEW B [Online] 92. Available at: https://doi.org/10.1103/PhysRevB.92.035139.

Slizovskiy, S., Betouras, J., Carr, S. and Quintanilla, J. (2014). Effect of paramagnetic fluctuations on a Fermisurface topological transition in two dimensions. Physical Review B [Online] 90:165110. Available at: http://dx.doi.org/10.1103/PhysRevB.90.165110.
We study the Fermisurface topological transition of the pocketopening type in a twodimensional Fermi liquid. We find that the paramagnetic fluctuations in an interacting Fermi liquid typically drive the transition first order at zero temperature. We first gain insight from a calculation using secondorder perturbation theory in the selfenergy. This is valid for weak interaction and far from instabilities. We then extend the results to stronger interaction, using the selfconsistent fluctuation approximation. Experimental signatures are given in light of our results.

Kainaris, N., Gornyi, I., Carr, S. and Mirlin, A. (2014). Conductivity of a generic helical liquid. PHYSICAL REVIEW B [Online] 90. Available at: https://doi.org/10.1103/PhysRevB.90.075118.

Mazo, V., Huang, C., Shimshoni, E., Carr, S. and Fertig, H. (2014). Superfluidinsulator transition of quantum Hall domain walls in bilayer graphene. Physical Review B  Condensed Matter and Materials Physics [Online] 89:121411121416. Available at: http://www.dx.doi.org/10.1103/PhysRevB.89.121411.
We consider the Î½=0 quantum Hall ferromagnetic state of bilayer graphene subject to a kinklike perpendicular electric field, which generates domain walls in the electronic state and lowenergy collective modes confined to move along them. In particular, it is shown that two pairs of collective helical modes are formed at opposite sides of the kink, each pair consisting of modes with identical helicities. We derive an effective fieldtheoretical model of these modes in terms of two weakly coupled anisotropic quantum spin ladders, with parameters tunable through control of the electric and magnetic fields. This yields a rich phase diagram, where, due to the helical nature of the modes, distinct phases possess very different charge conduction properties. Most notably, this system can potentially exhibit a transition from a superfluid to an insulating phase.

Schmitteckert, P., Carr, S. and Saleur, H. (2014). Transport through nanostructures: Finite time versus finite size. Physical Review B  Condensed Matter and Materials Physics [Online] 89:8140181406. Available at: http://www.dx.doi.org/10.1103/PhysRevB.89.081401.
Numerical simulations and experiments on nanostructures out of equilibrium usually exhibit strong finite size and finite measuring time tm effects. We discuss how these affect the determination of the full counting statistics for a general quantum impurity problem. We find that, while there are many methods available to improve upon finitesize effects, any realtime simulation or experiment will still be subject to finitetime effects: In short size matters, but time is limiting. We show that the leading correction to the cumulant generating function (CGF) at zero temperature for singlechannel quantum impurity problems is proportional to lntm, where the constant of proportionality is universally related to the steady state CGF itself for noninteracting systems; universal in this context means independent of details of the quench procedure, i.e., independent of the switching on of both voltage and counting field. We give detailed numerical evidence for the case of the selfdual interacting resonant level model that this relation survives the addition of interactions. This allows the extrapolation of finite measuring time in our numerics to the longtime limit, in excellent agreement with Betheansatz results.

Carr, S., Narozhny, B. and Nersesyan, A. (2013). Spinful fermionic ladders at incommensurate filling: Phase diagram, local perturbations, and ionic potentials. Annals of Physics [Online] 339:2280. Available at: http://www.dx.doi.org/10.1016/j.aop.2013.08.007.
We study the effect of external potential on transport properties of the fermionic twoleg ladder model. The response of the system to a local perturbation is strongly dependent on the ground state properties of the system and especially on the dominant correlations. We categorize all phases and transitions in the model (for incommensurate filling) and introduce "hoppingdriven transitions" that the system undergoes as the interchain hopping is increased from zero. We also describe the response of the system to an ionic potential. The physics of this effect is similar to that of the single impurity, except that the ionic potential can affect the bulk properties of the system and in particular induce true long range order.

Huang, C., Carr, S., Gutman, D., Shimshoni, E. and Mirlin, A. (2013). Transport via double constrictions in integer and fractional topological insulators. Physical Review B  Condensed Matter and Materials Physics [Online] 88:125134125134. Available at: http://www.scopus.com/inward/record.url?eid=2s2.084884869078&partnerID=40&md5=fdb35fde5df225a7b51b827083e83a4f.
We study transport properties of the helical edge states of twodimensional integer and fractional topological insulators via double constrictions. Such constrictions couple the upper and lower edges of the sample and can be made and tuned by adding side gates to the system. Using renormalization group and duality mapping, we analyze phase diagrams and transport properties in each of these cases. Most interesting is the case of two constrictions tuned to resonance, where we obtain Kondo behavior, with a tunable Kondo temperature. Moving away from resonance gives the possibility of a metalinsulator transition at some finite detuning. For integer topological insulators, this physics is predicted to occur for realistic interaction strengths and gives a conductance G with two temperature T scales where the sign of dG/dT changes, one being related to the Kondo temperature while the other is related to the detuning. Â© 2013 American Physical Society.

Carr, S., Fellows, J., Hooley, C. and Schmalian, J. (2012). Unbinding of Giant Vortices in States of Competing Order. Physical Review Letters: Moving Physics Forward [Online] 109:155703. Available at: http://dx.doi.org/10.1103/PhysRevLett.109.155703.
We consider a twodimensional system with two order parameters, one with O(2) symmetry and one with O(M), near a point in parameter space where they couple to become a single O(2+M) order. While the O(2) sector supports vortex excitations, these vortices must somehow disappear as the high symmetry point is approached. We develop a variational argument which shows that the size of the vortex cores diverges as 1/???? and the BerezinskiiKosterlitzThouless transition temperature of the O(2) order vanishes as 1/ln(1/?), where ? denotes the distance from the highsymmetry point. Our physical picture is confirmed by a renormalization group analysis which gives further logarithmic corrections, and demonstrates full symmetry restoration within the cores.

Schneider, M., Carr, S., Gornyi, I. and Mirlin, A. (2012). Weak localization and magnetoresistance in a twoleg ladder model. Physical Review B  condensed matter and materials physics [Online] 86:155141155158. Available at: http://www.dx.doi.org/10.1103/PhysRevB.86.155141.
We analyze the weaklocalization correction to the conductivity of a spinless twoleg ladder model in the limit of strong dephasing ? ?? tr,, paying particular attention to the presence of a magnetic field, which leads to an unconventional magnetoresistance behavior. We find that the magnetic field leads to three different effects: (i) negative magnetoresistance due to the regular weaklocalization correction, (ii) effective decoupling of the two chains, leading to positive magnetoresistance, and (iii) oscillations in the magnetoresistance originating from the nature of the lowenergy collective excitations. All three effects can be observed depending on the parameter range, but it turns out that large magnetic fields always decouple the chains and thus lead to the curious effect of magneticfieldenhanced localization.

Carr, S., Bagrets, D. and Schmitteckert, P. (2011). Full Counting Statistics in the SelfDual Interacting Resonant Level Model. Physical Review Letters [Online] 107:206801206801. Available at: http://dx.doi.org/10.1103/PhysRevLett.107.206801.
We present a general technique to obtain the zero temperature cumulant generating function of the full counting statistics of charge transfer in interacting impurity models out of equilibrium from timedependent simulations on a lattice. We demonstrate the technique with application to the selfdual interacting resonant level model, where very good agreement between numerical simulations using the density matrix renormalization group and those obtained analytically from the thermodynamic Bethe ansatz is found. We show from the exact form of counting statistics that the quasiparticles involved in transport carry charge 2e in the low bias regime and e/2 in the high bias regime.

Fellows, J. and Carr, S. (2011). Superfluid, solid, and supersolid phases of dipolar bosons in a quasionedimensional optical lattice. Physical Review A: Atomic, Molecular and Optical Physics [Online] 84:5160251607. Available at: http://www.dx.doi.org/10.1103/PhysRevA.84.051602.
We discuss a model of dipolar bosons trapped in a weakly coupled planar array of onedimensional tubes. We consider the situation where the dipolar moments are aligned by an external field, and we find a rich phase diagram as a function of the angle of this field exhibiting quantum phase transitions between solid, superfluid, and supersolid phases. In the low energy limit, the model turns out to be identical to one describing quasionedimensional superconductivity in condensed matter systems. This opens the possibility of using bosons as a quantum analog simulator of electronic systems, a scenario arising from the intricate relation between statistics and interactions in quasionedimensional systems.

Carr, S., Narozhny, B. and Nersesyan, A. (2011). Effect of a local perturbation in a fermionic ladder. Physical Review Letters: Moving Physics Forward [Online] 106:126805126809. Available at: http://www.dx.doi.org/10.1103/PhysRevLett.106.126805.
We study the effect of a local external potential on a system of two parallel spinpolarized nanowires placed close to each other. For singlechannel nanowires with repulsive interaction we find that transport properties of the system are highly sensitive to the transverse gradient of the perturbation: the asymmetric part completely reflects the electrons leading to vanishing conductance at zero temperature, while the flat potential remains transparent. We envisage a possible application of this unusual property in the sensitive measurement of local potential field gradients.

Carr, S., Quintanilla, J. and Betouras, J. (2010). Lifshitz transitions and crystallization of fully polarized dipolar fermions in an anisotropic twodimensional lattice. Physical Review B: Condensed Matter and Materials Physics [Online] 82:045110 1. Available at: http://dx.doi.org/10.1103/PhysRevB.82.045110.
We consider a twodimensional model of noninteracting chains of spinless fermions weakly coupled via a small interchain hopping and a repulsive interchain interaction. The phase diagram of this model has a surprising feature: an abrupt change in the Fermi surface as the interaction is increased. We study in detail this metanematic transition and show that the wellknown 21/2order Lifshitz transition is the critical end point of this firstorder quantum phase transition. Furthermore, in the vicinity of the end point, the order parameter has a nonperturbative BCStype form. We also study a competing crystallization transition in this model and derive the full phase diagram. This physics can be demonstrated experimentally in dipolar ultracold atomic or molecular gases. In the presence of a harmonic trap, it manifests itself as a sharp jump in the density profile.

Carr, S., Quintanilla, J. and Betouras, J. (2009). Deconfinement and Quantum Liquid Crystalline States of Dipolar Fermions in Optical Lattices. International Journal of Modern Physics B [Online] 23:40744086. Available at: http://dx.doi.org/10.1142/S0217979209063262.
We describe a simple model of fermions in quasione dimension that features interactioninduced deconfinement (a phase transition where the effective dimensionality of the system increases as interactions are turned on) and which can be realised using dipolar fermions in an optical lattice(1). The model provides a relisation of a "soft quantum matter" phase diagram of stronglycorrelated fermions, featuring metanematic, smectic and crystalline states, in addition to the normal Fermi liquid. In this paper we review the model and discuss in detail the mechanism behind each of these transitions on the basis of bosonization and detailed analysis of the RPA susceptibility.

Quintanilla, J., Carr, S. and Betouras, J. (2009). Metanematic, smectic, and crystalline phases of dipolar fermions in an optical lattice. Physical Review A: Atomic, Molecular and Optical Physics [Online] 79. Available at: http://dx.doi.org/10.1103/PhysRevA.79.031601.
It has been suggested that some strongly correlated matter might be understood qualitatively in terms of liquid crystalline phases intervening between the Fermi gas and the Wigner crystal or Mott insulator. We propose a tunable realization of this soft quantum matter physics in an ultracold gas. It uses optical lattices and dipolar interactions to realize a particularly simple model. Our analysis reveals a rich phase diagram featuring a metanematic transition where the Fermi liquid changes dimensionality; a smectic phase (stripes) and a crystalline "checkerboard" phase.

Carr, S. (2008). Strong correlation effects in singlewall carbon nanotubes. International Journal of Modern Physics B [Online] 22:52355260. Available at: http://www.dx.doi.org/10.1142/S0217979208049455.
We present an overview of strong correlations in singlewall carbon nanotubes, and an introduction to the techniques used to study them theoretically. We concentrate on zigzag nanotubes, although universality dictates that much of the theory can also be applied to armchair or chiral nanotubes. We show how interaction effects lead to exotic low energy properties and discuss future directions for studies on correlation effects in nanotubes.

Carr, S., Gogolin, A. and Nersesyan, A. (2007). Interaction induced dimerization in zigzag single wall carbon nanotubes. Physical Review B  Condensed Matter and Materials Physics [Online] 76:245121245130. Available at: http://www.dx.doi.org/10.1103/PhysRevB.76.245121.
We derive a lowenergy effective model of metallic zigzag carbon nanotubes at half filling. We show that there are three important features characterizing the lowenergy properties of these systems: the longrange Coulomb interaction, umklapp scattering, and an explicit dimerization generated by interactions. The ratio of the dimerization induced gap and the Mott gap induced by the umklapp interactions is dependent on the radius of the nanotube and can drive the system upon increasing dimerization strength from a Haldane spinliquid phase through a quantum phase transition with SU (2)1 quantum symmetry to a dimerized phase. We consider the physical properties of the phases on either side of this transition, which should be relevant for realistic nanotubes.

Carr, S., Narozhny, B. and Nersesyan, A. (2006). Spinless fermionic ladders in a magnetic field: Phase diagram. Physical Review B  Condensed Matter and Materials Physics [Online] 73:195114195128. Available at: http://www.dx.doi.org/10.1103/PhysRevB.73.195114.
The system of interacting spinless fermions hopping on a twoleg ladder exhibits a series of quantum phase transitions when subjected to an external magnetic field. At halffilling, these are either U(1) Gaussian phase transitions between two phases with distinct types of longrange order or BerezinskiiKosterlitzThouless transitions between ordered and gapless phases.

Narozhny, B., Carr, S. and Nersesyan, A. (2005). Fractional charge excitations in fermionic ladders. Physical Review B: Condensed Matter and Materials Physics [Online] 71:161101161105. Available at: http://www.dx.doi.org/10.1103/PhysRevB.71.161101.
The system of interacting spinless fermions hopping on a twoleg ladder in the presence of an external magnetic field is shown to possess a longrange order: the bond density wave or the staggered flux phase. In both cases the elementary excitations are Z2 kinks and carry one half the charge of an electron. Â© 2005 The American Physical Society.

Carr, S. and Tsvelik, A. (2003). Spectrum and correlation functions of a quasionedimensional quantum Ising model. Physical Review Letters: Moving Physics Forward [Online] 90:177206177210. Available at: http://www.dx.doi.org/10.1103/PhysRevLett.90.177206.
The dynamical susceptibility was studied, focusing on the region of the phase diagram well below the transition line where new nonuniversal physics can be found. It was shown that some of the beautiful physics of the quantum Ising model in a magnetic field with a hidden E8 symmetry may be observed even in a realistic quasionedimensional model in its ordered phase far from the transition line.

Carr, S. and Tsvelik, A. (2002). Superconductivity and chargedensity waves in a quasionedimensional spingap system. Physical Review B: Condensed Matter and Materials Physics [Online] 65:195121195131. Available at: http://www.dx.doi.org/10.1103/PhysRevB.65.195121.
We consider a model of spingapped chains weakly coupled by Josephson and Coulomb interactions. Combining such nonperturbative methods as bosonization and the Bethe ansatz to treat the intrachain interactions with the random phase approximation for the interchain couplings and the first corrections to this, we investigate the phase diagram of this model. The phase diagram shows both chargedensity wave ordering and superconductivity. These phases are separated by line of critical points which exhibits an approximate SU(2) symmetry. We consider the effects of a magnetic field on the system. We apply the theory to the material Sr2Ca12Cu24O41 and suggest further experiments.