10 research outputs found
Non-dissipative anomalous currents in 2D materials: the parity magnetic effect as an analog of the chiral magnetic effect
Anomalous electric currents along a magnetic field, first predicted to emerge
during large heavy ion collision experiments, were also observed a few years
ago in condensed matter environments, exploring the fact that charge carriers
in Dirac/Weyl semi-metals exhibit a relativistic-like behavior. The mechanism
through which such currents are generated relies on an imbalance in the
chirality of systems immersed in a magnetic background, leading to the
so-called chiral magnetic effect (CME). While chiral magnetic currents have
been observed in materials in three space dimensions, in this work we propose
that an analog of the chiral magnetic effect can be constructed in two space
dimensions, corresponding to a novel type of intrinsic half-integer Quantum
Hall effect, thereby also offering a topological protection mechanism for the
current. While the 3D chiral anomaly underpins the CME, its 2D cousin is
emerging from the 2D parity anomaly, we thence call it the parity magnetic
effect (PME). It can occur in disturbed honeycomb lattices where both spin
degeneracy and time reversal symmetry are broken. These configurations harbor
two distinct gap-opening mechanisms that, when occurring simultaneously, drive
slightly different gaps in each valley, establishing an analog of the necessary
chiral imbalance. Some examples of promising material setups that fulfill the
prerequisites of our proposal are also listed.Comment: 11 pages, 5 figure
Cavity effects on the Fermi velocity renormalization in a graphene sheet
Recently, in the literature, it was shown that the logarithmic renormalization of the Fermi velocity in a plane graphene sheet (which, in turn, is related to the Coulombian static potential associated to electrons in the sheet) is inhibited by the presence of a single parallel conducting plate. In the present paper, we investigate the situation of a suspended graphene sheet in a cavity formed by two conducting plates parallel to the sheet. The effect of a cavity on the interaction between electrons in the graphene is not merely the addition of the effects of each plate individually. From this, one can expect that the inhibition of the renormalization of the Fermi velocity generated by a cavity is not a mere addition of the inhibition induced by each single plate. In other words, the simple addition of the result for the inhibition of the renormalization of the Fermi velocity found in the literature for a single plate could not be used to predict the exact behavior of the inhibition for the graphene between two plates. Here, we show that, in fact, this is what happens and calculate how the presence of a cavity formed by two conducting plates parallel to the suspended graphene sheet amplifies, in a non-additive manner, the inhibition of the logarithmic renormalization of the Fermi velocity. In the limits of a single plate and no plates, our formulas recover those found in the literature.This work was partially supported by the following Brazilian Agencies: Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES), Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq), and Fundacao de Amparo a Pesquisa do Estado do Rio de Janeiro (FAPERJ). E. C. Marino was partially supported by CNPq and FAPERJ. D. T. Alves was partially supported by CAPES via Programa Estagio Senior no Exterior - Processo 88881.119705/2016-01, by CNPq via Processos 461826/2014-3 (Edital Universal) and 311920/2014-4 (Bolsa de Produtividade em Pesquisa), and also thanks Jaime Santos, Mikhail I. Vasilevskiy, Nuno M. R. Peres and Yuliy Bludov for useful discussions, as well as the hospitality of the Centro de Fisica, Universidade do Minho, Braga - Portugal. V. S. Alves acknowledges CNPq for support through Bolsa de Produtividade em Pesquisa n. 312654/2017-0. The authors also thank Ygor P. Silva for useful comments
Field and Gauge Theories with Ultracold Gauge Potentials and Fields
In the last decade there has been an intense activity aimed at the quantum simulation of interacting
many-body systems using cold atoms [1, 2]. The idea of quantum simulations traces back to Feynman
[3], who argued that the ideal setting to study quantum systems would be a quantum experimental
setup rather then a classical one - the latter one being fundamentally limited due to its hardware classical
structure. This is a particularly important problem given the intrinsic complexity of interacting
many-body problems, and the difficulties that arise when tackling them with numerical simulations -
two paradigmatic examples being the sign(s) problem affecting Monte Carlo simulations of fermionic
systems, and the real time dynamics in more than one spatial dimension.
Ultracold atoms offer a very powerful setting for quantum simulations. Atoms can be trapped
in tailored optical and magnetic potentials, also controlling their dimensionality. The inter-atomic
interactions can be tuned by external knobs, such as Feshbach resonances. This gives a large freedom
on model building and, with suitable mappings, they allow the implementation of desired target models.
This allowed an impressive exploitation of quantum simulators on the context of condensed matter
physics.
The simulation of high-energy physics is an important line of research in this field and it is less
direct. In particular it requires the implementation of symmetries like Lorentz and gauge invariance
which are not immediately available in a cold atomic setting. Gauge fields are ubiquitous in
physics ranging from condensed matter [4\u20136] and quantum computation [7, 8] to particle physics [9],
an archetypical example being Quantum Chromodynamics (QCD) [10,11], the theory of strong nuclear
forces. Currently open problems in QCD, providing a long-term goal of cold atomic simulations, include
confinement/deconfinement and the structure of color superconducting phases at finite chemical
potential [12]. Even though QCD is a very complicated theory (to simulate or study), it is possible
to envision a path through implementation of simpler models. Furthermore, it is also expected that
interesting physics is found on such \u201cintermediate models\u201d which may deserve attention irrespectively
of the QCD study. A very relevant model in this regard is the Schwinger model (Quantum Electrodynamics
in 1+1 dimensions) [13]. This theory exhibits features of QCD, such as confinement [14],
and is at the very same time amenable to both theoretical studies and simpler experimental schemes.
This model was the target of the first experimental realization of a gauge theory with a quantum
simulator [15].
The work on this Thesis is, in part, motivated by the study of toy models which put in evidence
certain aspects that can be found in QCD. Such toy models provide also intermediate steps in the
path towards more complex simulations. The two main aspects of QCD which are addressed here
are symmetry-locking and confinement. The other main motivation for this study is to develop a
systematic framework, through dimensional mismatch, for theoretical understanding and quantum
simulations of long-range theories using gauge theories.
The model used to study symmetry-locking consists of a four-fermion mixture [16]. It has the basic
ingredients to exhibit a non-Abelian symmetry-locked phase: the full Hamiltonian has an SU (2)
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SU (2) (global) symmetry which can break to a smaller SU (2) group. Such phase is found in a extensive
region of the phase diagram by using a mean-field approach and a strong coupling expansion. A possible
realization of such system is provided by an Ytterbium mixture. Even without tuning interactions,
it is shown that such mixture falls inside the the locked-symmetry phase pointing towards a possible
realization in current day experiments.
The models with dimensional mismatch investigated here have fermions in a lower dimensionality
d + 1 and gauge fields in higher dimensionality D + 1. They serve two purposes: establish mappings
to non-local theories by integration of fields [17] and the study of confinement [18].
In the particular case of d = 1 and D = 2 it is found that some general non-local terms can be
obtained on the Lagrangian [17]. This is found in the form of power-law expansions of the Laplacian
mediating either kinetic terms (for bosons) or interactions (for fermions). The fact that such expansions
are not completely general is not surprising since constraints do exist, preventing unphysical features
like breaking of unitarity. The non-local terms obtained are physically acceptable, in this regard, since
they are derived from unitary theories. The above mapping is done exactly. In certain cases it is
shown that it is possible to construct an effective long-range Hamiltonian in a perturbative expansion.
In particular it is shown how this is done for non-relativistic fermions (in d = 1) and 3 + 1 gauge
fields. These results are relevant in the context of state of the art experiments which implement
models with long-range interactions and where theoretical results are less abundant than for the case
of local theories. The above mappings establish a direct relation with local theories which allow
theoretical insight onto these systems. Examples of this would consist on the application of Mermin-
Wagner-Hohenberg theorem [19, 20] and Lieb-Robinson bounds [21], on the propagation of quantum
correlations, to non-local models. In addition they can also provide a path towards implementation of
tunable long-range interactions with cold atoms. Furthermore, in terms of quantum simulations, they
are in between the full higher dimensional system and the full lower dimensional one. Such property is
attractive from the point of view of a gradual increase of complexity for quantum simulations of gauge
theories.
Another interesting property of these models is that they allow the study of confinement beyond the
simpler case of the Schwinger model. The extra dimensions are enough to attribute dynamics to the
gauge field, which are no longer completely fixed by the Gauss law. The phases of the Schwinger model
are shown to be robust under variation of the dimension of the gauge fields [18]. Both the screened
phase, of the massless case, and the confined phase, of the massive one, are found for gauge fields in
2+1 and 3+1 dimensions. Such results are also obtained in the Schwinger- Thirring model. This shows
that these phases are very robust and raises interesting questions about the nature of confinement.
Robustness under Thirring interactions are relevant because it shows that errors on the experimental
implementation will not spoil the phase. Even more interesting is the case of gauge fields in higher
dimensions since confinement in the Schwinger model is intuitively atributed to the dimensionality of
the gauge fields (creating linear potentials between particles).
This Thesis is organized as follows. In Chapter 1, some essential background regarding quantum
simulations of gauge theories is provided. It gives both a brief introduction to cold atomic physics and
lattice gauge theories. In Chapter 2, it is presented an overview over proposals of quantum simulators
of gauge potentials and gauge fields. At the end of this Chapter, in Section 2.3 it is briefly presented
ongoing work on a realization of the Schwinger model that we term Half Link Schwinger model. There,
it is argued, some of the generators of the gauge symmetry on the lattice can be neglected without
comprimising gauge invariance. In Chapter 3, the results regarding the phase diagram of the fourfermion
mixture, exhibiting symmetry-locking, is presented. In Chapter 4, the path towards controlling
non-local kinetic terms and interactions is provided, after a general introduction to the formalism of
dimensional mismatch. At the end the construction of effective Hamiltonians is described. Finally,
Chapter 5 concerns the study of confinement and the robustness of it for 1+1 fermions. The first part
regards the Schwinger-Thirring with the presence of a -term while, in the second part, models with
dimensional mismatch are considered. The thesis ends with conclusions and perspectives of future
work based on the results presented here
Finite group lattice gauge theories for quantum simulation
The present manuscript focuses on Lattice Gauge Theories based on finite groups. For the purpose of Quantum Simulation, the Hamiltonian approach is considered, while the finite group serves as a discretization scheme for the degrees of freedom of the gauge fields. Several aspects of these models are studied. First, we investigate dualities in Abelian models with a restricted geometry, using a systematic approach. This leads to a rich phase diagram dependent on the super-selection sectors. Second, we construct a family of lattice Hamiltonians for gauge theories with a finite group, either Abelian or non-Abelian. We show that is possible to express the electric term as a natural graph Laplacian, and that the physical Hilbert space can be explicitly built using spin network states. In both cases we perform numerical simulations in order to establish the correctness of the theoretical results and further investigate the models