Large Quantum Fluctuations Research Articles

Low-dimensional magnetic properties of the ladder-like polynuclear complex Cu2(naphac)2(OH)2 (naphac = 3-(1-naphthyl)acrylate)

The polynuclear complex Cu2(naphac)2(OH)2 consists of isolated Cu ladders in which square planar CuO4 and square-pyramidal CuO5 units are linked alternately along the crystalline a direction through their corners, and the resultant two adjacent Cu alternating chains connect each other through edges of the CuO5 units to form a ladder. The temperature dependence of the magnetic susceptibility above 50 K is reproduced by the calculation of the spin-1/2 two-leg honeycomb spin ladder model with almost zero exchange coupling between two legs of ladder. This is explained by the Jahn-Teller elongation of square-pyramidal CuO5 units. The absence of lambda-shaped peak in the specific heat down to 1.9 K suggests the existence of large quantum fluctuations of the spin owing to low-dimensional antiferromagnetic interactions.

Quantum spin liquid signatures in monolayer 1T-NbSe2

Quantum spin liquids (QSLs) are in a quantum disordered state that is highly entangled and has fractional excitations. As a highly sought-after state of matter, QSLs were predicted to host spinon excitations and to arise in frustrated spin systems with large quantum fluctuations. Here we report on the experimental observation and theoretical modeling of QSL signatures in monolayer 1T-NbSe2, which is a newly emerging two-dimensional material that exhibits both charge-density-wave (CDW) and correlated insulating behaviors. By using scanning tunneling microscopy and spectroscopy (STM/STS), we confirm the presence of spin fluctuations in monolayer 1T-NbSe2 by observing the Kondo resonance as monolayer 1T-NbSe2 interacts with metallic monolayer 1H-NbSe2. Subsequent STM/STS imaging of monolayer 1T-NbSe2 at the Hubbard band energy further reveals a long-wavelength charge modulation, in agreement with the spinon modulation expected for QSLs. By depositing manganese-phthalocyanine (MnPc) molecules with spin S = 3/2 onto monolayer 1T-NbSe2, new STS resonance peaks emerge at the Hubbard band edges of monolayer 1T-NbSe2. This observation is consistent with the spinon Kondo effect induced by a S = 3/2 magnetic impurity embedded in a QSL. Taken together, these experimental observations indicate that monolayer 1T-NbSe2 is a new promising QSL material.

Tearing down spacetime with quantum disentanglement

A longstanding enigma within AdS/CFT concerns the entanglement entropy of holographic quantum fields in Rindler space. The vacuum of a quantum field in Minkowski spacetime can be viewed as an entangled thermofield double of two Rindler wedges at a temperature T = 1/2π. We can gradually disentangle the state by lowering this temperature, and the entanglement entropy should vanish in the limit T → 0 to the Boulware vacuum. However, holography yields a non-zero entanglement entropy at arbitrarily low T, since the bridge in the bulk between the two wedges retains a finite width. We show how this is resolved by bulk quantum effects of the same kind that affect the entropy of near-extremal black holes. Specifically, a Weyl transformation maps the holographic Boulware states to near-extremal hyperbolic black holes. A reduction to an effective two-dimensional theory captures the large quantum fluctuations in the geometry of the bridge, which bring down to zero the density of entangled states in the Boulware vacuum. Using another Weyl transformation, we construct unentangled Boulware states in de Sitter space.

Smooth extensions of black holes in loop quantum gravity

Vacuum spherically symmetric loop quantum gravity in the midi-superspace approximation using inhomogeneous horizon-penetrating slices has been studied for a decade, and it has been noted that the singularity is eliminated. It is replaced by a region of high curvature and potentially large quantum fluctuations. It was recently pointed out that the effective semiclassical metric implies the existence of a shell of matter which violates energy conditions in regions where the curvature is largest. Here, we propose an alternative way of treating the problem that is free from the shells. The ambiguity in the treatment is related with the existence of new observables in the quantum theory that characterize the area excitations, and how the counterpart of diffeomorphisms in the discrete quantum theory is mapped to the continuum semiclassical picture. The resulting spacetime in the high curvature region inside the horizon is approximated by a metric of the type of the Simpson–Visser wormhole and it connects the black hole interior to a white hole in a smooth manner.

Formation of trapped vacuum bubbles during inflation, and consequences for PBH scenarios

A class of inflationary scenarios for primordial black hole (PBH) formation include a small barrier in the slope of the potential. There, the inflaton slows down, generating an enhancement of primordial perturbations. Moreover, the background solution overcomes the barrier at a very low speed, and large backward quantum fluctuations can prevent certain regions from overshooting the barrier. This leads to localized bubbles where the field remains “trapped” behind the barrier. In such models, therefore, we have two distinct channels for PBH production: the standard adiabatic density perturbation channel and the bubble channel. Here, we perform numerical simulations of bubble formation, addressing the issues of initial conditions, critical amplitude and bubble expansion. Further, we explore the scaling behaviour of the co-moving size of bubbles with the initial amplitude of the field fluctuation. We find that for small to moderate non-Gaussianity f NL ≲ 2.6, the threshold for the formation of vacuum bubbles agrees with previous analytical estimates [1] to 5% accuracy or so. We also show that the mass distribution for the two channels is different, leading to a slightly broader range of PBH masses when both contributions are comparable. The bubble channel is subdominant for small f NL, and becomes dominant for f NL ≳ 2.6. We find that the mass of PBHs in the bubble channel is determined by an adiabatic overdensity surrounding the bubble at the end of inflation. Remarkably, the profile of this overdensity turns out to be of type-II. This represents a first clear example showing that overdensities of type-II can be dominant in comparison with the standard type-I. We also comment on exponential tails and on the fact that in models with local type non-Gaussianity (such as the one considered here), the occurrence of alternative channels can easily be inferred from unitarity considerations.

Primordial black holes and stochastic inflation beyond slow roll. Part I. Noise matrix elements

Primordial Black Holes (PBHs) may form in the early Universe, from the gravitational collapse of large density perturbations, generated by large quantum fluctuations during inflation. Since PBHs form from rare over-densities, their abundance is sensitive to the tail of the primordial probability distribution function (PDF) of the perturbations. It is therefore important to calculate the full PDF of the perturbations, which can be done non-perturbatively using the `stochastic inflation' framework. In single field inflation models generating large enough perturbations to produce an interesting abundance of PBHs requires violation of slow roll. It is therefore necessary to extend the stochastic inflation formalism beyond slow roll. A crucial ingredient for this are the stochastic noise matrix elements of the inflaton potential. We carry out analytical and numerical calculations of these matrix elements for a potential with a feature which violates slow roll and produces large, potentially PBH generating, perturbations. We find that the transition to an ultra slow-roll phase results in the momentum induced noise terms becoming larger than the field noise whilst each of them falls exponentially for a few e-folds. The noise terms then start rising with their original order restored, before approaching constant values which depend on the nature of the slow roll parameters in the post transition epoch. This will significantly impact the quantum diffusion of the coarse-grained inflaton field, and hence the PDF of the perturbations and the PBH mass fraction.

From spin liquid to magnetic ordering in the anisotropic kagome Y-kapellasite Y3Cu9(OH)19Cl8 : A single-crystal study

Y${}_{3}$Cu${}_{9}$(OH)${}_{19}$Cl${}_{8}$, also known as Y-kapellasite, realizes an original anisotropic frustrated kagome model. Here, the authors study large phase-pure single crystals, obtained via an external gradient method, by susceptibility, specific heat, thermal expansion, neutron scattering, and local $\ensuremath{\mu}$SR and NMR techniques. These find subtle structural changes along with long-range magnetic ordering (1/3,1/3). Large quantum fluctuations reduce the Cu${}^{2+}$ moments, likely as a result of the proximity to a phase boundary in the rich magnetic phase diagram of the model.

First-Principles Thermodynamics of CsSnI3.

CsSnI3 is a promising ecofriendly solution for energy harvesting technologies. It exists at room temperature in either a black perovskite polymorph or a yellow 1D double-chain, which irreversibly deteriorates in the air. In this work, we unveil the relative thermodynamic stability between the two structures with a first-principles sampling of the CsSnI3 finite-temperature phase diagram, discovering how it is driven by anomalously large quantum and anharmonic ionic fluctuations. Thanks to a comprehensive treatment of anharmonicity, the simulations deliver a remarkable agreement with known experimental data for the transition temperatures of the orthorhombic, rhombohedral, and cubic perovskite structures and the thermal expansion coefficient. We disclose how the perovskite polymorphs are the ground state above 270 K and discover an abnormal decrease in heat capacity upon heating in the cubic black perovskite. Our results also significantly downplay the Cs+ rattling modes' contribution to mechanical instability. The remarkable agreement with experiments validates our methodology, which can be systematically applied to all metal halides.

Schwinger boson theory of ordered magnets

The Schwinger boson theory provides a natural path for treating quantum spin systems with large quantum fluctuations. In contrast to semi-classical treatments, this theory allows us to describe a continuous transition between magnetically ordered and spin liquid states, as well as the continuous evolution of the corresponding excitation spectrum. The square lattice Heisenberg antiferromagnet is one of the first models that was approached with the Schwinger boson theory. Here we revisit this problem to reveal several subtle points that were omitted in previous treatments and that are crucial to further develop this formalism. These points include the freedom for the choice of the saddle point (Hubbard-Stratonovich decoupling and choice of the condensate) and the $1/N$ expansion in the presence of a condensate. A key observation is that the spinon condensate leads to Feynman diagrams that include contributions of different order in $1/N$, which must be accounted to get a qualitatively correct excitation spectrum. We demonstrate that a proper treatment of these contributions leads to an exact cancellation of the single-spinon poles of the dynamical spin structure factor, as expected for a magnetically ordered state. The only surviving poles are the ones arising from the magnons (two-spinon bound states), which are the true collective modes of an ordered magnet.

Quantum statistical fluctuation of energy and its novel pseudo-gauge dependence

We discuss the quantum statistical fluctuations of energy in subsystems of hot relativistic gas for both spin-zero and spin-half particles. We explicitly show the system size dependence of the quantum statistical fluctuation of energy. Our results show that with decreasing system size quantum statistical fluctuations increase substantially. As the consistency of the framework, we also argue that the quantum statistical fluctuations give rise to the known result for statistical fluctuation of energy in the canonical ensemble if we consider the size of the subsystem to be sufficiently large. For a spin-half particle, quantum fluctuations show some interesting novel features. We show that within a small sub-system quantum statistical fluctuation of energy for spin-half particles depends on the various pseudo-gauge choices of the energy-momentum tensor. Interestingly, for sufficiently large subsystems quantum fluctuations obtained for different pseudo-gauge choices converge and we recover the canonical-ensemble formula known for statistical fluctuations of energy. Our calculation is very general and can be applied to any branch of physics whenever one deals with a thermal system. As a practical application, we argue that our results can be used to determine a coarse-graining scale to introduce the concept of classical energy density or fluid element relevant for the strongly interacting matter, in particular for small systems produced in heavy-ion collisions.

Primordial Weibel instability

We study the onset of vector instabilities in the post-inflationary epoch of the Universe as a mechanism for primordial magnetic fields amplification.We assume the presence of a charged spectator scalar field arbitrarily coupled to gravity during Inflation in its vacuum de Sitter state. Gravitational particle creation takes place at the transition from Inflation to the subsequent Reheating stage and thus the vacuum field state becomes an excited many particles one.Consequently this state can be described as a real fluid, and we build out the hydrodynamic framework using second order theories for relativistic fluids with a relaxation time prescription for the collision integral.Given the high-temperature regime and the vanishing scalar curvature of the Universe during Reheating (radiation-dominated-type era), the fluid can be regarded as a conformal one.The large quantum fluctuations induced by the rapid transition from inflationary to effectively radiation dominated expansion become statistical fluctuations whereby both a charge excess and anisotropic pressures are produced in any finite domain. The precise magnitude of the effect for each scale is determined by the size of the averaging domain and the coupling to curvature. We look at domains which are larger than the horizon at the beginning of Reheating, but much smaller than our own horizon, and show that in a finitefraction of them the anisotropy and charge excess provide suitable conditions for a Weibel instability. If moreover the duration of reheating is shorter than the relaxation time of the fluid, then this instability can compensate or even overcome the conformal dilution of a primordial magnetic field. We show that the non-trivial topology of the magnetic field encoded in its magnetic helicity is also amplified if present.

Midisuperspace foam and the cosmological constant

Wheeler’s conjectured ‘spacetime foam’—large quantum fluctuations of spacetime at the Planck scale—could have important implications for quantum gravity, perhaps even explaining why the cosmological constant seems so small. Here I explore this problem in a midisuperspace model consisting of metrics with local spherical symmetry. Classically, an infinite class of ‘foamy’ initial data can be constructed, in which cancellations between expanding and contracting regions lead to a small average expansion even if Λ is large. Quantum mechanically, the model admits corresponding stationary states, for which the probability current is also nearly zero. These states appear to describe a self-reproducing spacetime foam with very small average expansion, effectively hiding the cosmological constant.

Physical properties of YbFe5P3 with a quasi-one-dimensional crystal structure

We report basic physical properties of the quasi-one-dimensional heavy-fermion compound $\mathrm{Yb}{\mathrm{Fe}}_{5}{\mathrm{P}}_{3}$. Its magnetic susceptibility follows a modified Curie-Weiss behavior at high temperatures with a Weiss temperature between $\ensuremath{-}5$ and $\ensuremath{-}21$ K depending on the direction of the applied magnetic field. Our single crystals of $\mathrm{Yb}{\mathrm{Fe}}_{5}{\mathrm{P}}_{3}$ are good metals with a room-temperature resistivity of $\ensuremath{\sim}140$ $\ensuremath{\mu}\mathrm{\ensuremath{\Omega}}$ cm and a residual resistivity of less than 2 $\ensuremath{\mu}\mathrm{\ensuremath{\Omega}}$ cm. Below $\ensuremath{\sim}2$ K the resistivity reflects the presence of strong quantum fluctuations, which is supported by specific heat measurements that show a similar strong enhancement in $C/T$ at low temperatures reaching 1.5 J/mol ${\mathrm{K}}^{2}$ below $T=0.5$ K. No magnetic ordering is observed down to 80 mK. Magnetic fields up to 8 T rapidly suppress the magnetic fluctuations, while resistivity measurements under pressures up to 2.54 GPa indicate the enhancement of quantum fluctuations, although still no order is observed down to 0.3 K. Density functional theory calculations suggest the presence of electronically quasi-one-dimensional (1D) Fermi surface sheets together with three-dimensional electronic pockets. We suggest that the quasi-1D nature of this compound leads to an extended regime of large quantum fluctuations within the paramagnetic state prior to reaching a magnetic instability.

Robust Topological Order in Fermionic Z2 Gauge Theories: From Aharonov-Bohm Instability to Soliton-Induced Deconfinement

Topologically-ordered phases of matter, although stable against local perturbations, are usually restricted to relatively small regions in phase diagrams. Their preparation requires thus a precise fine tunning of the system's parameters, a very challenging task in most experimental setups. In this work, we investigate a model of spinless fermions interacting with dynamical $\mathbb{Z}_2$ gauge fields on a cross-linked ladder, and show evidence of topological order throughout the full parameter space. In particular, we show how a magnetic flux is spontaneously generated through the ladder due to an Aharonov-Bohm instability, giving rise to topological order even in the absence of a plaquette term. Moreover, the latter coexists here with a symmetry-protected topological phase in the matter sector, that displays fractionalised gauge-matter edge states, and intertwines with it by a flux-threading phenomenon. Finally, we unveil the robustness of these features through a gauge frustration mechanism, akin to geometric frustration in spin liquids, allowing topological order to survive to arbitrarily large quantum fluctuations. In particular, we show how, at finite chemical potential, topological solitons are created in the gauge field configuration, which bound to fermions forming $\mathbb{Z}_2$ deconfined quasi-particles. The simplicity of the model makes it an ideal candidate where 2D gauge theory phenomena, as well as exotic topological effects, can be investigated using cold-atom quantum simulators.

Quantum cluster quasicrystals

Quasicrystals remain among the most intriguing materials in physics and chemistry. Their structure results in many unusual properties including anomalously low friction as well as poor electrical and thermal conductivity but it also supports superconductivity, which shows that quantum effects in quasicrystals can be quite unique. Here we theoretically study superfluidity in a model quantum cluster quasicrystal. Using path-integral Monte Carlo simulations, we explore a 2D ensemble of bosons with the Lifshitz-Petrich-Gaussian pair potential, finding that moderate quantum fluctuations do not destroy the dodecagonal quasicrystalline order. This quasicrystal is characterized by a small yet finite superfluidity, demonstrating that particle clustering combined with the local cogwheel structure can underpin superfluidity even in the almost classical regime. This type of distributed superfluidity may also be expected in certain open crystalline lattices. Large quantum fluctuations are shown to induce transitions to cluster solids, supersolids and superfluids, which we characterize fully quantum-mechanically.

On stochastic effects and primordial black-hole formation

The effect of large quantum fluctuations on primordial black-hole formation for inflationary models with a quasi-inflection point is investigated. By using techniques of stochastic inflation in combination with replica field theory and the Feynman–Jensen variational method, it is non-perturbatively demonstrated that the abundance of primordial black holes is amplified by several orders of magnitude as compared to the classical computation.

Large off-diagonal exchange couplings and spin liquid states in C3 -symmetric iridates

Iridate oxides on a honeycomb lattice are considered promising candidates for realization of quantum spin liquid states. We investigate the magnetic couplings in a structural model for a honeycomb iridate K$_2$IrO$_3$, with $C_3$ point group symmetry at the Ir sites, which is an end member of the recently synthesized iridate family K$_x$Ir$_y$O$_2$. Using \textit{ab-initio} quantum chemical methods, we elucidate the subtle relationship between the real space symmetry and magnetic anisotropy and show that the higher point group symmetry leads to high frustration with strong magnetic anisotropy driven by the unusually large off-diagonal exchange couplings ($\Gamma$'s) as opposed to other spin-liquid candidates considered so far. Consequently, large quantum fluctuations imply lack of magnetic ordering consistent with the experiments. Exact diagonalization calculations for the fully anisotropic $K$-$J$-$\Gamma$ Hamiltonian reveal the importance of the off-diagonal anisotropic exchange couplings in stabilizing a spin liquid state and highlight an alternative route to stabilize spin liquid states for ferromagnetic $K$.

Are there Goldstone bosons in d≤z+1 ?

We study the viability of spontaneous breaking of continuous symmetries in theories with Lifshitz scaling, according to the number of space-time dimensions $d$ and the dynamical scaling $z$. Then, the answer to the question in the title is no (quantum field theoretically) and yes (holographically). With field theory tools, we show that symmetry breaking is indeed prevented by large quantum fluctuations when $d\leq z+1$, as expected from scaling arguments. With holographic tools, on the other hand, we find nothing that prevents the existence of a vacuum expectation value. This difference is made possible by the large $N$ limit of holography. An important subtlety in this last framework is that in order to get a proper description of a conserved current, renormalization of the temporal mode of the bulk vector requires an alternative quantization. We also comment on the implications of turning on temperature.

Quantum parametric resonance of a dissipative oscillator: fading and persistent memory in the long-time evolution

The evolution of a quantum oscillator, with periodically varying frequency and damping, is studied in the two cases of parametric resonance (PR) producing a limited, or unlimited stretching of the wave function. The different asymptotic behaviors of the energy distribution, show the non-trivial interplay between PR and the initial quantum state. In the first case, the oscillator’s mean energy tends asymptotically to a fully classical value, independently of the initial state, with vanishing relative quantum fluctuations. In the second case, the memory of the initial state persists over arbitrary long time scales, both in the mean value and in the large quantum fluctuations of the energy.

Parametric Excitation of a Bose-Einstein Condensate: From Faraday Waves to Granulation

We explore, both experimentally and theoretically, the response of an elongated Bose-Einstein condensate to modulated interactions. We identify two distinct regimes differing in modulation frequency and modulation strength. Longitudinal surface waves are generated either resonantly or parametrically for modulation frequencies near the radial trap frequency or twice the trap frequency, respectively. The dispersion of these waves, the latter being a Faraday wave, is well-reproduced by a mean-field theory that accounts for the 3D nature of the elongated condensate. In contrast, in the regime of lower modulation frequencies we find that no clear resonances occur, but with increased modulation strength, the condensate forms an irregular granulated distribution that is outside the scope of a mean-field approach. We find that the granulated condensate is characterized by large quantum fluctuations and correlations, which are well-described with single-shot simulations obtained from wavefunctions computed by a beyond mean-field theory at zero temperature, the multiconfigurational time-dependent Hartree for bosons method.