Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLong-range multi-scalar models at three loops
341
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We compute the three-loop beta functions of long-range multi-scalar models with general quartic interactions. The long-range nature of the models is encoded in a kinetic term with a Laplacian to the power $0<zeta<1$, rendering the computation of Feynman diagrams much harder than in the usual short-range case ($zeta=1$). As a consequence, previous results stopped at two loops, while six-loop results are available for short-range models. We push the renormalization group analysis to three loops, in an $epsilon=4zeta-d$ expansion at fixed dimension $d<4$, extensively using the Mellin-Barnes representation of Feynman amplitudes in the Schwinger parametrization. We then specialize the beta functions to various models with different symmetry groups: $O(N)$, $(mathbb{Z}_2)^N rtimes S_N$, and $O(N)times O(M)$. For such models, we compute the fixed points and critical exponents.
rate research
Read More
We study the second-order phase transition in the $d$-dimensional Ising model with long-range interactions decreasing as a power of the distance $1/r^{d+s}$. For $s$ below some known value $s_*$, the transition is described by a conformal field theory without a local stress tensor operator, with critical exponents varying continuously as functions of $s$. At $s=s_*$, the phase transition crosses over to the short-range universality class. While the location $s_*$ of this crossover has been known for 40 years, its physics has not been fully understood, the main difficulty being that the standard description of the long-range critical point is strongly coupled at the crossover. In this paper we propose another field-theoretic description which, on the contrary, is weakly coupled near the crossover. We use this description to clarify the nature of the crossover and make predictions about the critical exponents. That the same long-range critical point can be reached from two different UV descriptions provides a new example of infrared duality.
Inspired by Fr{o}hlich-Spencer and subsequent authors who introduced the notion of contour for long-range systems, we provide a definition of contour and a direct proof for the phase transition for ferromagnetic long-range Ising models on $mathbb{Z}^d$, $dgeq 2$. The argument, which is based on a multi-scale analysis, works for the sharp region $alpha>d$ and improves previous results obtained by Park for $alpha>3d+1$, and by Ginibre, Grossmann, and Ruelle for $alpha> d+1$, where $alpha$ is the power of the coupling constant. The key idea is to avoid a large number of small contours. As an application, we prove the persistence of the phase transition when we add a polynomial decaying magnetic field with power $delta>0$ as $h^*|x|^{-delta}$, where $h^* >0$. For $d<alpha<d+1$, the phase transition occurs when $delta>d-alpha$, and when $h^*$ is small enough over the critical line $delta=d-alpha$. For $alpha geq d+1$, $delta>1$ it is enough to prove the phase transition, and for $delta=1$ we have to ask $h^*$ small. The natural conjecture is that this region is also sharp for the phase transition problem when we have a decaying field.
We analyze the quantum phases, correlation functions and edge modes for a class of spin-1/2 and fermionic models related to the 1D Ising chain in the presence of a transverse field. These models are the Ising chain with anti-ferromagnetic long-range interactions that decay with distance $r$ as $1/r^alpha$, as well as a related class of fermionic Hamiltonians that generalise the Kitaev chain, where both the hopping and pairing terms are long-range and their relative strength can be varied. For these models, we provide the phase diagram for all exponents $alpha$, based on an analysis of the entanglement entropy, the decay of correlation functions, and the edge modes in the case of open chains. We demonstrate that violations of the area law can occur for $alpha lesssim1$, while connected correlation functions can decay with a hybrid exponential and power-law behaviour, with a power that is $alpha$-dependent. Interestingly, for the fermionic models we provide an exact analytical derivation for the decay of the correlation functions at every $alpha$. Along the critical lines, for all models breaking of conformal symmetry is argued at low enough $alpha$. For the fermionic models we show that the edge modes, massless for $alpha gtrsim 1$, can acquire a mass for $alpha < 1$. The mass of these modes can be tuned by varying the relative strength of the kinetic and pairing terms in the Hamiltonian. Interestingly, for the Ising chain a similar edge localization appears for the first and second excited states on the paramagnetic side of the phase diagram, where edge modes are not expected. We argue that, at least for the fermionic chains, these massive states correspond to the appearance of new phases, notably approached via quantum phase transitions without mass gap closure. Finally, we discuss the possibility to detect some of these effects in experiments with cold trapped ions.
The QED$_3$-Gross-Neveu model is a (2+1)-dimensional U(1) gauge theory involving Dirac fermions and a critical real scalar field. This theory has recently been argued to represent a dual description of the deconfined quantum critical point between Neel and valence bond solid orders in frustrated quantum magnets. We study the critical behavior of the QED$_3$-Gross-Neveu model by means of an epsilon expansion around the upper critical space-time dimension of $D_c^+=4$ up to the three-loop order. Estimates for critical exponents in 2+1 dimensions are obtained by evaluating the different Pade approximants of their series expansion in epsilon. We find that these estimates, within the spread of the Pade approximants, satisfy a nontrivial scaling relation which follows from the emergent SO(5) symmetry implied by the duality conjecture. We also construct explicit evidence for the equivalence between the QED$_3$-Gross-Neveu model and a corresponding critical four-fermion gauge theory that was previously studied within the 1/N expansion in space-time dimensions 2<D<4.
In recent years, dynamical phase transitions and out-of-equilibrium criticality have been at the forefront of ultracold gases and condensed matter research. Whereas universality and scaling are established topics in equilibrium quantum many-body physics, out-of-equilibrium extensions of such concepts still leave much to be desired. Using exact diagonalization and the time-dependent variational principle in uniform martrix product states, we calculate the time evolution of the local order parameter and Loschmidt return rate in transverse-field Ising chains with antiferromagnetic power law-decaying interactions, and map out the corresponding rich dynamical phase diagram. textit{Anomalous} cusps in the return rate, which are ubiquitous at small quenches within the ordered phase in the case of ferromagnetic long-range interactions, are absent within the accessible timescales of our simulations. We attribute this to much weaker domain-wall binding in the antiferromagnetic case. For quenches across the quantum critical point, textit{regular} cusps appear in the return rate and connect to the local order parameter changing sign, indicating the concurrence of two major concepts of dynamical phase transitions. Our results consolidate conclusions of previous works that a necessary condition for the appearance of anomalous cusps in the return rate after quenches within the ordered phase is for topologically trivial local spin flips to be the energetically dominant excitations in the spectrum of the quench Hamiltonian. Our findings are readily accessible in modern trapped-ion setups, and we outline the associated experimental considerations.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
