Topological physics in quantum critical systems

The onset of ordering in quantum critical systems is characterized by a competition between the Kondo shielding of magnetic moments and the ordering of these moments. We show how a distribution of Kondo shielding temperatures—resulting from chemical doping—leads to critical behavior whose main characteristics are given by percolation physics. With the aid of Monte Carlo computer simulations, we are able to infer the low temperature part of the distribution of shielding temperatures in heavily doped quantum critical Ce(Ru0.24Fe0.76)2Ge2. Based on this distribution, we show that the ordering dynamics—such as the growth of the correlation length upon cooling—can be understood by the spawning of magnetic clusters. Our findings explain why the search for universal exponents in quantum critical systems has been unsuccessful: the underlying percolation network associated with the chemical doping of quantum critical systems has to be incorporated in the modeling of these quantum critical systems.

We present neutron-scattering results on the magnetic excitations in the spinel compounds Lix[Mn1.96Li0.04]O4 (x=0.2,0.6,0.8,1.0). We show that the dominant excitations below T?70?K are determined by Mn ions located in clusters, and that these excitations mimic the dynamic scaling found in quantum critical systems that also harbor magnetic clusters, such as CeRu0.5Fe1.5Ge2. We argue that our results for this classical spinel compound suggest that the unusual response at low temperatures as observed in quantum critical systems that have been driven to criticality through substantial chemical doping is (at least) partially the result of the fragmentation of the magnetic lattice into smaller units.

The presence of magnetic clusters has been verified in both antiferromagnetic and ferromagnetic quantum critical systems. We review some of the strongest evidence for strongly doped quantum critical systems (Ce(Ru0.24Fe0.76)2Ge2) and we discuss the implications for the response of the system when cluster formation is combined with finite size effects. In particular, we discuss the change of universality class that is observed close to the order-disorder transition. We detail the conditions under which clustering effects will play a significant role also in the response of stoichiometric systems and their experimental signature.

Conversions between the ground states in quantum critical systems via entanglement-assisted local operations and classical communications (ELOCC) are studied. We propose an alternative method to reveal the different convertibility by local operations when a quantum phase transition occurs. We have studied the ground-state local convertibility in the one-dimensional transverse field Ising model, $XY$ model and $XXZ$ model. It is found that the ELOCC convertibility suddenly changes at the phase transition points. In the transverse field Ising model the ELOCC convertibility between the first-excited state and the ground state are also distinct for different phases. The relation between the order of quantum phase transitions and the local convertibility is discussed.

In this series of works, we study exactly solvable non-unitary time evolutions in one-dimensional quantum critical systems ranging from quantum quenches to time-dependent drivings. In this part I, we are motivated by the recent works of Kontsevich and Segal (2021 arXiv:2105.10161) and Witten (2021 arXiv:2111.06514) on allowable complex spacetime metrics in quantum field theories. In general, such complex spacetime metrics will lead to non-unitary time evolutions. In this work, we study the universal features of such non-unitary time evolutions based on exactly solvable setups. Various physical quantities including the entanglement Hamiltonian and entanglement spectrum, entanglement entropy, and energy density at an arbitrary time can be exactly solved. Due to the damping effect introduced by the complex time, the excitations in the initial state are gradually damped out in time. The non-equilibrium dynamics exhibit universal features that are qualitatively different from the case of real-time evolutions. For instance, for an infinite system after a global quench, the entanglement entropy of the semi-infinite subsystem will grow logarithmically in time, in contrast to the linear growth in a real-time evolution. Moreover, we study numerically the time-dependent driven quantum critical systems with allowable complex spacetime metrics. It is found that the competition between driving and damping leads to a steady state with an interesting entanglement structure.

The most basic local conversion is local operations and classical communications (LOCC), which is also the most natural restriction in quantum information processing. We investigate the conversions between the ground states in quantum critical systems via LOCC and propose a novel method to reveal the different convertibilities via majorization relation when a quantum phase transition occurs. The ground-state local convertibility in the one-dimensional transverse field Ising model is studied. It is shown that the LOCC convertibility changes nearly at the phase transition point. The relation between the order of quantum phase transitions and the LOCC convertibility is discussed. Our results are compared with the corresponding results by using the Rényi entropy and the LOCC convertibility with assisted entanglement.

We study the entanglement between disjoint subregions in quantum critical systems through the lens of the logarithmic negativity. We work with systems in arbitrary dimensions, including conformal field theories and their corresponding lattice Hamiltonians, as well as resonating valence-bond states. At small separations, the logarithmic negativity is big and displays universal behavior, but we show nonperturbatively that it decays faster than any power at large separations. This can already be seen in the minimal setting of single-spin subregions. The corresponding absence of distillable entanglement at large separations generalizes the one-dimensional result, and indicates that quantum critical ground states do not possess long-range bipartite entanglement, at least for bosons. For systems with fermions, a more suitable definition of the logarithmic negativity exists that takes into account fermion parity, and we show that it decays algebraically. Along the way we obtain general results for the moments of the partially transposed density matrix. Published by the American Physical Society 2024

In a D=2+1 quantum critical system, the entanglement entropy across a boundary with a corner contains a subleading logarithmic scaling term with a universal coefficient. It has been conjectured that this coefficient is, to leading order, proportional to the number of field components N in the associated O(N) continuum $\phi^4$ field theory. Using density matrix renormalization group calculations combined with the powerful numerical linked cluster expansion technique, we confirm this scenario for the O(2) Wilson-Fisher fixed point in a striking way, through direct calculation at the quantum critical points of two very different microscopic models. The value of this corner coefficient is, to within our numerical precision, twice the coefficient of the Ising fixed point. Our results add to the growing body of evidence that this universal term in the R\'enyi entanglement entropy reflects the number of low-energy degrees of freedom in a system, even for strongly interacting theories.

Quantum critical systems are extremely sensitive to parameter variation near the critical point. Moreover, the derivatives with respect to the order parameter may exhibit divergence. This quantum criticality is widely utilized to enhance the performance of quantum metrology. In this study, we take the dissipative quantum Rabi model (QRM) as an example and use the bath-engineering technique to simulate the dissipative QRM to explore the impact of the quantum criticality on the quantum metrology under dissipation. We numerically calculate the dynamics of the inverse variance of the dissipative QRM around the critical point by using the quantum-simulation method and compare our results with those obtained by the numerically exact hierarchical equations of motion (HEOM). Our simulations show that in the case of the strong dissipation or the high temperature, the precision does not exhibit divergence when approaching the point of the quantum phase transition, and the enhancement of quantum metrology by quantum criticality is relatively limited. More importantly, the quantum-simulation method based on the bath-engineering technique can accurately simulate the dynamical evolution of the critical system and consumes significantly fewer resources as compared with the HEOM. Thus, it can be an alternative solution for investigating the dynamical evolution of larger critical systems for quantum metrology.

The halon is a special critical state of an impurity in a quantum-critical environment. The hallmark of the halon physics is that a well-defined integer charge gets fractionalized into two parts: a microscopic core with half-integer charge and a critically large halo carrying a complementary charge of $\pm 1/2$. The halon phenomenon emerges when the impurity--environment interaction is fine-tuned to the vicinity of a boundary quantum critical point (BQCP), at which the energies of two quasiparticle states with adjacent integer charges approach each other. The universality class of such BQCP is captured by a model of pseudo-spin-$1/2$ impurity coupled to the quantum-critical environment, in such a way that the rotational symmetry in the pseudo-spin $xy$-plane is respected, with a small local "magnetic" field along the pseudo-spin $z$-axis playing the role of control parameter driving the system away from the BQCP. On the approach to BQCP, the half-integer projection of the pseudo-spin on its $z$-axis gets delocalized into a halo of critically divergent radius, capturing the essence of the phenomenon of charge fractionalization. With large-scale Monte Carlo simulations, we confirm the existence of halons---and quantify their universal features---in O(2) and O(3) quantum critical systems.

We compute the ratio of the pairing gap $\Delta$ at $T=0$ and $T_c$ for a set of quantum-critical models in which the pairing interaction is mediated by a gapless boson with local susceptibility $\chi (\Omega) \propto 1/|\Omega|^\gamma$ (the $\gamma$ model). The limit $\gamma = 0+$ ($\chi (\Omega) =\log {|\Omega|}$) describes color superconductivity, and models with $\gamma >0$ describe superconductivity in a metal at the onset of charge or spin order. The ratio $2\Delta/T_c$ has been recently computed numerically for $0<\gamma <2$ within Eliashberg theory and was found to increase with increasing $\gamma$ [T-H Lee et al, arXiv:1805.10280]. We argue that the origin of the increase is the divergence of $2\Delta/T_c$ at $\gamma =3$. We obtain an approximate analytical formula for $2\Delta/T_c$ for $\gamma \leq 3$ and show that it agrees well with the numerics. We also consider in detail the opposite limit of small $\gamma$. Here we obtain the explicit expressions for $T_c$ and $\Delta$, including numerical prefactors. We show that these prefactors depend on fermionic self-energy in a rather non-trivial way. The ratio $2\Delta/T_c$ approaches the BCS value $3.53$ at $\gamma \to 0$.

Currents through quantum systems may probe non-analyticities in\nquantum-critical many-body ground states. For a large class of dissipative\nquantum critical systems we show that it is possible to obtain the reduced\nsystem dynamics in the vicinity of quantum critical points in a\nthermodynamically consistent way, while capturing non-Markovian effects. We\nachieve this by combining reaction coordinate mappings with polaron transforms.\nExemplarily, we consider the Lipkin-Meshkov-Glick model in a transport setup,\nwhere the quantum phase transition manifests itself in the heat transfer\nstatistics.\n

We study entanglement via the subsystem purity relative to bipartitions of arbitrary excited states in (1+1)-dimensional conformal field theory, equivalent to the scaling limit of one dimensional quantum critical systems. We compute the exact subpurity as a function of the relative subsystem size for numerous excited states in the Ising and three-state Potts models. We find that it decays exponentially when the system and the subsystem sizes are comparable until a saturation limit is reached near half-partitioning, signaling that excited states are maximally entangled. The exponential behavior translates into extensivity for the second R\'enyi entropy. Since the coefficient of this linear law depends only on the excitation energy, this result shows an interesting, new relationship between energy and quantum information and elucidates the role of microscopic details.

The experimental observation of quantum phase transitions predicted by the quantum Rabi model in quantum critical systems is usually challenging due to the lack of signature experimental observables associated with them. Here, we describe a method to identify the dynamical critical phenomenon in the quantum Rabi model consisting of a three-level atom and a cavity at the quantum phase transition. Such a critical phenomenon manifests itself as a sudden change of steady-state output photons in the system driven by two classical fields, when both the atom and the cavity are initially unexcited. The process occurs as the high-frequency pump field is converted into the low-frequency Stokes field and multiple cavity photons in the normal phase, while this conversion cannot occur in the superradiant phase. The sudden change of steady-state output photons is an experimentally accessible measure to probe quantum phase transitions, as it does not require preparing the equilibrium state.

In this paper, using the Gauge/gravity duality techniques, we explore the hydrodynamic regime of a very special class of strongly coupled QFTs that come up with an emerging UV length scale in the presence of a negative hyperscaling violating exponent. The dual gravitational counterpart for these QFTs consists of scalar dressed black brane solutions of exactly integrable Einstein-scalar gravity model with Domain Wall (DW) asymptotics. In the first part of our analysis we compute the $ R $-charge diffusion for the boundary theory and find that (unlike the case for the pure $ AdS_{4} $ black branes) it scales quite non trivially with the temperature. In the second part of our analysis, we compute the $ \eta/s $ ratio both in the non extremal as well as in the extremal limit of these special class of gauge theories and it turns out to be eqaul to $ 1/4\pi $ in both the cases. These results therefore suggest that the quantum critical systems in the presence of (negative) hyperscaling violation at UV, might fall under a separate universality class as compared to those conventional quantum critical systems with the usual $ AdS_4 $ duals.