In the presence of strong spinindependent interactions and spinorbit coupling, we show that the spinor Bose liquid confined to one spatial dimension undergoes an interaction or densitytuned quantum phase transition similar to one theoretically proposed for itinerant magnetic solidstate systems. The order parameter describes broken Z_{2}inversion symmetry, with the ordered phase accompanied by nonvanishing momentum which is generated by fluctuations of an emergent dynamical gauge field at the phase transition. This quantum phase transition has dynamical critical exponent
Continuous N\'{e}elVBS quantum phase transition in nonlocal onedimensional systems with SO(3) symmetry
One dimensional (1d) interacting systems with local Hamiltonianscan be studied with various welldeveloped analytical methods.Recently novel 1d physics was found numerically in systems witheither spatially nonlocal interactions, or at the 1d boundary of2d quantum critical points, and the critical fluctuation in thebulk also yields effective nonlocal interactions at the boundary.This work studies the edge states at the 1d boundary of 2dstrongly interacting symmetry protected topological (SPT) states,when the bulk is driven to a disorderorder phase transition. Wewill take the 2d AffleckKennedyLiebTasaki (AKLT) state as anexample, which is a SPT state protected by the SO(3) spinsymmetry and spatial translation. We found that the original(1+1)d boundary conformal field theory of the AKLT state isunstable due to coupling to the boundary avatar of the bulkquantum critical fluctuations. When the bulk is fixed at thequantum critical point, within the accuracy of our expansionmethod, we find that by tuning one parameter at the boundary,there is a generic direct transition between the long rangeantiferromagnetic Néel order and the valence bond solid (VBS)order. This transition is very similar to the NéelVBStransition recently found in numerical simulation of a spin1/2chain with nonlocal spatial interactions. Connections between ouranalytical studies and recent numerical results concerning theedge states of the 2d AKLTlike state at a bulk quantum phasetransition will also be discussed.
more »
« less
 Award ID(s):
 1920434
 NSFPAR ID:
 10229671
 Date Published:
 Journal Name:
 SciPost Physics
 Volume:
 10
 Issue:
 2
 ISSN:
 25424653
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
More Like this

Abstract z ≃ 2, typical of a Lifshitz transition, but is described by a nontrivial interacting fixed point. From direct numerical simulation of the microscopic model, we extract previously unknown critical exponents for this fixed point. Our model describes a realistic situation of 1D ultracold atoms with Ramaninduced spinorbit coupling, establishing this system as a platform for studying exotic critical behavior of the HertzMillis type. 
A bstract We develop a mathematical theory of symmetry protected trivial (SPT) orders and anomalyfree symmetry enriched topological (SET) orders in all dimensions via two different approaches with an emphasis on the second approach. The first approach is to gauge the symmetry in the same dimension by adding topological excitations as it was done in the 2d case, in which the gauging process is mathematically described by the minimal modular extensions of unitary braided fusion 1categories. This 2d result immediately generalizes to all dimensions except in 1d, which is treated with special care. The second approach is to use the 1dimensional higher bulk of the SPT/SET order and the boundarybulk relation. This approach also leads us to a precise mathematical description and a classification of SPT/SET orders in all dimensions. The equivalence of these two approaches, together with known physical results, provides us with many precise mathematical predictions.more » « less

It is known that the classical O(N) O ( N ) model in dimension d > 3 d gt; 3 at its bulk critical point admits three boundary universality classes:the ordinary, the extraordinary and the special. For the ordinarytransition the bulk and the boundary order simultaneously; theextraordinary fixed point corresponds to the bulk transition occurringin the presence of an ordered boundary, while the special fixed pointcorresponds to a boundary phase transition between the ordinary and theextraordinary classes. While the ordinary fixed point survives in d = 3 d = 3 ,it is less clear what happens to the extraordinary and special fixedpoints when d = 3 d = 3 and N \ge 2 N ≥ 2 .Here we show that formally treating N N as a continuous parameter, there exists a critical value N_c > 2 N c gt; 2 separating two distinct regimes. For 2 \leq N < N_c 2 ≤ N < N c the extraordinary fixed point survives in d = 3 d = 3 ,albeit in a modified form: the longrange boundary order is lost,instead, the order parameter correlation function decays as a power of \log r log r .For N > N_c N gt; N c there is no fixed point with order parameter correlations decayingslower than power law. We discuss several scenarios for the evolution ofthe phase diagram past N = N_c N = N c .Our findings appear to be consistent with recent Monte Carlo studies ofclassical models with N = 2 N = 2 and N = 3 N = 3 .We also compare our results to numerical studies of boundary criticalityin 2+1D quantum spin models.more » « less

In this paper we propose a special type of a tree tensor network that has the geometry of a comb—a onedimensional (1D) backbone with finite 1D teeth projecting out from it. This tensor network is designed to provide an effective description of higherdimensional objects with special limited interactions or, alternatively, onedimensional systems composed of complicated zerodimensional objects. We provide details on the best numerical procedures for the proposed network, including an algorithm for variational optimization of the wave function as a comb tensor network and the transformation of the comb into a matrix product state. We compare the complexity of using a comb versus alternative matrix product state representations using density matrix renormalization group algorithms. As an application, we study a spin1 Heisenberg model system which has a comb geometry. In the case where the ends of the teeth are terminated by spin1/2 spins, we find that Haldane edge states of the teeth along the backbone form a critical spin1/2 chain, whose properties can be tuned by the coupling constant along the backbone. By adding nextnearestneighbor interactions along the backbone, the comb can be brought into a gapped phase with a longrange dimerization along the backbone. The critical and dimerized phases are separated by a KosterlitzThouless phase transition, the presence of which we confirm numerically. Finally, we show that when the teeth contain an odd number of spins and are not terminated by spin1/2's, a special type of comb edge states emerge.more » « less

BACKGROUND Landau’s Fermi liquid theory provides the bedrock on which our understanding of metals has developed over the past 65 years. Its basic premise is that the electrons transporting a current can be treated as “quasiparticles”—electronlike particles whose effective mass has been modified, typically through interactions with the atomic lattice and/or other electrons. For a long time, it seemed as though Landau’s theory could account for all the manybody interactions that exist inside a metal, even in the socalled heavy fermion systems whose quasiparticle mass can be up to three orders of magnitude heavier than the electron’s mass. Fermi liquid theory also lay the foundation for the first successful microscopic theory of superconductivity. In the past few decades, a number of new metallic systems have been discovered that violate this paradigm. The violation is most evident in the way that the electrical resistivity changes with temperature or magnetic field. In normal metals in which electrons are the charge carriers, the resistivity increases with increasing temperature but saturates, both at low temperatures (because the quantized lattice vibrations are frozen out) and at high temperatures (because the electron mean free path dips below the smallest scattering pathway defined by the lattice spacing). In “strange metals,” by contrast, no saturation occurs, implying that the quasiparticle description breaks down and electrons are no longer the primary charge carriers. When the particle picture breaks down, no local entity carries the current. ADVANCES A new classification of metallicity is not a purely academic exercise, however, as strange metals tend to be the hightemperature phase of some of the best superconductors available. Understanding hightemperature superconductivity stands as a grand challenge because its resolution is fundamentally rooted in the physics of strong interactions, a regime where electrons no longer move independently. Precisely what new emergent phenomena one obtains from the interactions that drive the electron dynamics above the temperature where they superconduct is one of the most urgent problems in physics, attracting the attention of condensed matter physicists as well as string theorists. One thing is clear in this regime: The particle picture breaks down. As particles and locality are typically related, the strange metal raises the distinct possibility that its resolution must abandon the basic building blocks of quantum theory. We review the experimental and theoretical studies that have shaped our current understanding of the emergent strongly interacting physics realized in a host of strange metals, with a special focus on their posterchild: the copper oxide hightemperature superconductors. Experiments are highlighted that attempt to link the phenomenon of nonsaturating resistivity to parameterfree universal physics. A key experimental observation in such materials is that removing a single electron affects the spectrum at all energy scales, not just the lowenergy sector as in a Fermi liquid. It is observations of this sort that reinforce the breakdown of the singleparticle concept. On the theoretical side, the modern accounts that borrow from the conjecture that strongly interacting physics is really about gravity are discussed extensively, as they have been the most successful thus far in describing the range of physics displayed by strange metals. The foray into gravity models is not just a pipe dream because in such constructions, no particle interpretation is given to the charge density. As the breakdown of the independentparticle picture is central to the strange metal, the gravity constructions are a natural tool to make progress on this problem. Possible experimental tests of this conjecture are also outlined. OUTLOOK As more strange metals emerge and their physical properties come under the scrutiny of the vast array of experimental probes now at our disposal, their mysteries will be revealed and their commonalities and differences cataloged. In so doing, we should be able to understand the universality of strange metal physics. At the same time, the anomalous nature of their superconducting state will become apparent, offering us hope that a new paradigm of pairing of nonquasiparticles will also be formalized. The correlation between the strength of the linearintemperature resistivity in cuprate strange metals and their corresponding superfluid density, as revealed here, certainly hints at a fundamental link between the nature of strange metallicity and superconductivity in the cuprates. And as the gravityinspired theories mature and overcome the challenge of projecting their powerful mathematical machinery onto the appropriate crystallographic lattice, so too will we hope to build with confidence a complete theory of strange metals as they emerge from the horizon of a black hole. Curved spacetime with a black hole in its interior and the strange metal arising on the boundary. This picture is based on the string theory gaugegravity duality conjecture by J. Maldacena, which states that some strongly interacting quantum mechanical systems can be studied by replacing them with classical gravity in a spacetime in one higher dimension. The conjecture was made possible by thinking about some of the fundamental components of string theory, namely Dbranes (the horseshoeshaped object terminating on a flat surface in the interior of the spacetime). A key surprise of this conjecture is that aspects of condensed matter systems in which the electrons interact strongly—such as strange metals—can be studied using gravity.more » « less