arXiv subjects

Sung-Sik Lee

Publications and source records attributed to Sung-Sik Lee.

At least 19 recordsLinked to original sources

arXiv2026

Emergent time and more from wavefunction collapse in general relativity

In this paper, we further develop a recently proposed theory of time based on wavefunction collapse in general relativity. It is based on the postulations that quantum states, which violate the momentum and Hamiltonian constraints, represent instances of time, and stochastic fluctuations of the lapse and shift generate the time evolution under which an initial state gradually collapses toward a diffeomorphism-invariant state. Under the wavefunction collapse, the scale factor monotonically increases, thus acting as a clock. The scalar, vector, and tensor gravitons arise as physical excitations, and the arrow of time for their evolution is set by the initial state. In the long-time limit, the tensor gravitons exhibit emergent unitary dynamics. However, the extra modes are strongly damped due to the non-unitary dynamics that suppress the constraint-violating excitations. The vector mode is uniformly suppressed over all length scales, but the decay rate of the scalar is proportional to its wave vector. This makes the latter a viable candidate for dark matter; excitations with large wavelengths survive over long periods, contributing to long-range interactions, while the fast decay of short-wavelength modes renders them undetectable without sufficient temporal resolution. These are demonstrated for the cosmological constant-dominated universe through semi-classical and adiabatic approximations, which are controlled in the limit of large space dimension.

gr-qc↗

arXiv2026

Classification of non-Fermi liquids and universal superconducting fluctuations

In quantum critical metals, a plethora of different non-Fermi liquids arises depending on the nature of critical fluctuations coupled to Fermi surfaces. In this paper, we classify non-Fermi liquids that arise from q=0 critical fluctuations and characterize their universal superconducting fluctuations. The essential tool is the projective fixed points, which generalizes the notion of fixed points to fixed trajectories that take into account the incessant running of the Fermi momentum under the renormalization group flow. Based on the topology of bundles of projective fixed points, non-Fermi liquids are first grouped into seven superuniversality classes. Each superuniversality class includes multiple universality classes, which are further classified by the universal pairing interactions and emergent symmetries. Despite the pairing interaction generated by critical fluctuations, some non-Fermi liquids remain stable down to zero temperature due to the incoherence of excitations and the lack of scale invariance caused by Fermi momentum. Depending on the strength and span of the universal pairing interaction in momentum space, the emergent symmetry of non-Fermi liquids may or may not be lower than that of Fermi liquids. In non-Fermi liquids that become superconductors at low temperatures, the universal data of the parent metal determine the lower bound for the superconducting transition temperature and the associated pairing symmetry. In superuniversality classes that contain non-Fermi liquids prone to non-s-wave superconducting instabilities, the critical angular momentum above which pairing instability becomes inevitable is sensitive to the Fermi momentum, and the associated superconducting transition temperature oscillates as a function of the density. We use physical examples, as well as a toy model, to elucidate the universal low-energy physics of all superuniversality classes.

cond-mat.str-el↗

arXiv2025

A theory of time based on wavefunction collapse

We propose that moments of time arise through the failed emergence of the temporal diffeomorphism as gauge symmetry, and that the passage of time is a continual process of an instantaneous state collapsing toward a gauge-invariant state. Unitarity and directedness of the resulting time evolution are demonstrated for a minisuperspace model of cosmology.

gr-qc↗

arXiv2025

Quantum criticality in cuprate superconductors revealed by optical conductivity measurement

The ubiquitous temperature ($T$)-linear behaviour of the transport scattering rate in the normal state of strongly correlated electron systems is called strange metallicity \cite{zaanen:2004,phillips:2022,hartnoll:2022,chowdhury:2022,yuan:2022}. Although strange metallicity is crucial to understanding superconductivity in correlated electron systems, its origin remains elusive to date \cite{hussey:2023}. Here, we present the doping-, temperature-, and frequency ($ω$)-dependent transport properties of overdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ in a wide doping range of 0.183 to 0.231. We observe that the optical scattering rate and effective mass exhibit an $ω/T$ scaling behaviour at a critical doping of $p_{c} \simeq$ 0.231. Away from the critical doping, the $ω/T$ scaling behaviour is destroyed below a doping-dependent crossover temperature $T_Δ(p) \sim |p-p_{c}|^{0.24}$. Furthermore, the optical coherence mode (OCM) observed within the superconducting dome rapidly broadens and eventually disappears as the critical doping is approached. The emergence of the $ω/T$ scaling behaviour of the transport scattering rate and broadening of the OCM near the critical doping strongly suggests that strange metallic behaviour is caused by quantum critical fluctuations. Our results provide compelling spectroscopic evidence for quantum criticality in cuprate superconductors.

cond-mat.supr-con↗

arXiv2025

Ultraviolet/infrared mixing-driven suppression of Kondo screening in the antiferromagnetic quantum critical metal

We study a magnetic impurity immersed in the two-dimensional antiferromagnetic quantum critical metal (AFQCM), using the field-theoretic functional renormalization group. Critical spin fluctuations represented by a bosonic field compete with itinerant electrons to couple with the impurity through the spin-spin interaction. At long distances, the antiferromagnetic electron-impurity (Kondo) coupling dominates over the boson-impurity coupling. However, the Kondo screening is weakened by the boson with an increasing severity as the hot spots connected by the magnetic ordering wave-vector are better nested. For $v_{0,i} \ll 1$, where $v_{0,i}$ is the bare nesting angle at the hot spots, the temperature $T_K^{\mathrm{AFQCM}}$ below which Kondo coupling becomes $O(1)$ is suppressed as $\frac{\log Λ/T_K^{\mathrm{AFQCM}}}{\log Λ/T_K^{\mathrm{FL}}} \sim \frac{g_{f,i}}{v_{0,i} \log 1/v_{0,i} }$, where $T_K^{\mathrm{FL}}$ is the Kondo temperature of the Fermi liquid with the same electronic density of states, and $g_{f,i}$ is the boson-impurity coupling defined at UV cutoff energy $Λ$. The remarkable efficiency of the single collective field in hampering the screening of the impurity spin by the Fermi surface originates from a ultraviolet/infrared (UV/IR) mixing: bosons with momenta up to a UV cutoff actively suppress Kondo screening at low energies.

cond-mat.str-el↗

arXiv2025

Dynamical kinetic energy quenching in the antiferromagnetic quantum critical metals

We study the dynamics of critical spin fluctuations and hot electrons at the metallic antiferromagnetic quantum critical points with $Z_2$ and $O(2)$ spin symmetries, building upon earlier works on the $O(3)$ symmetric theory. The interacting theories in $2+1$ dimensions are approached from $3+1$-dimensional theories in the $ε$-expansion that tunes the co-dimension of Fermi surface as a control parameter. The low-energy physics of the $Z_2$ and $O(2)$ theories qualitatively differ from each other and also from that of the $O(3)$ theory. The difference is caused by higher-order quantum corrections beyond the one-loop order that are important even to the leading order in $ε$. The naive loop-expansion breaks down due to dynamical quenching of kinetic energy: the speed of the collective mode ($c$) and the Fermi velocity perpendicular to the magnetic ordering vector ($v$) become vanishingly small at low energies. What sets the three theories apart is the hierarchy that emerges between the quenched kinetic terms. At the infrared fixed point, $c/v$ becomes $0$, $1$ and $\infty$ in the $Z_2$, $O(2)$ and $O(3)$ theories, respectively. At intermediate energy scales, the slow renormalization group (RG) flows of $c$ and $v$ toward their fixed point values create approximate scale invariance controlled by approximate marginal parameters. The manifold of those quasi-fixed points and the RG flow therein determines crossovers from scaling behaviours with transient critical exponents at intermediate energy scales to the universal scaling in the low-energy limit. If the symmetry group is viewed as a tuning parameter, the $O(2)$ theory corresponds to a multi-critical point which has one additional quasi-marginal parameter than the other two theories.

cond-mat.str-el↗

arXiv2024

Space of non-Fermi liquids

In metals, low-energy effective theories are characterized by a set of coupling functions. Among them, the angle-dependent Fermi momentum specifies the size and shape of Fermi surface. Since the Fermi momentum grows incessantly under the renormalization group flow, a metallic fixed point is defined only modulo a rescaling of Fermi momentum. In this paper, we discuss the physical consequences of this projective nature of fixed points for non-Fermi liquids with hot Fermi surfaces. The first is the absence of a unique dynamical critical exponent that dictates the relative scaling between energy and momentum. The second is mismatches between the scaling dimensions of couplings and their relevancy. Nonetheless, each projective fixed point is characterized by a few marginal and relevant coupling functions, and the notion of universality survives. We illustrate our findings by charting the space of projective fixed points and extracting their universal properties for the Ising-nematic quantum critical metal beyond the patch theory. To control the theory, we use the dimensional regularization scheme that tunes the co-dimension of Fermi surface. Near the upper critical dimension, two exactly marginal coupling functions span the space of stable projective fixed points: functions that specify the shape of the Fermi surface and the angle-dependent Fermi velocity. All other coupling functions, including the Landau functions and the universal pairing interaction, are fixed by those two marginal functions. With decreasing dimensions, the forward scattering remains irrelevant while the pairing interaction becomes relevant near two dimensions. In two dimensions, it is expected that the universal superconducting fluctuations lower the symmetry of the non-Fermi liquid realized above the superconducting transition temperatures from the loop U(1) group to a proper subgroup.

cond-mat.str-el↗

arXiv2023

Emergence of curved momentum-spacetime and its effect on the cyclotron motion in the antiferromagnetic quantum critical metal

We show that anisotropic quantum corrections can dynamically give rise to curved momentum-spacetimes for quasiparticles in metals. In the (2+1)-dimensional antiferromagnetic quantum critical metal, a curved momentum-spacetime arises as the critical spin fluctuations generate red shift that dilates frequency of electron unevenly on the Fermi surface. As the disparity of the momentum-dependent red shift is controlled by the shape of the Fermi surface, the momentum-spacetime geometry that emerges at low energies depends on the bare nesting angle of the Fermi surface. With increasing nesting angle, the region in which electron motion is slowed down by critical spin fluctuations shrinks. On the other hand, the increasing nesting angle makes the red shift stronger near the hot spots due to the weakened screening of the interaction. These competing effects result in a non-monotonic dependence of the cyclotron frequency of electron on the nesting angle of the Fermi surface. The red shift that becomes more singular at the hot spots with increasing nesting angle creates a possibility of realizing a momentum-space black hole horizon beyond a critical nesting angle : the electron motion becomes `perpetually' slowed down as it approaches a hot spot in the same way that the motion of a free falling object freezes near the event horizon of a black hole with respect to an asymptotic observer. However, the analogous horizon in momentum space does not lead to a vanishing cyclotron frequency because the metric singularity at the hot spots is cut off by thermal effects present above the non-zero superconducting transition temperature.

cond-mat.str-el↗

arXiv2023

Anomalous quasiparticle lifetime in geometric quantum critical metals

Metals can undergo geometric quantum phase transitions where the local curvature of the Fermi surface changes sign without a change in symmetry or topology. At the inflection points on the Fermi surface, the local curvature vanishes, leading to an anomalous dynamics of quasiparticles. In this paper, we study geometric quantum critical metals that support inflection points in two dimensions, and show that the decay rate of quasiparticles goes as $E^α$ with $1<α<2$ as a function of quasiparticle energy $E$ at the inflection points.

cond-mat.str-el↗

arXiv2023

Fermi liquids beyond the forward scattering limit: the role of non-forward scatterings for scale invariance and instabilities

Landau Fermi liquid theory is a fixed point theory of metals that includes the forward scattering amplitudes as exact marginal couplings. However, the fixed point theory that only includes the strict forward scatterings is non-local in real space. In this paper, we revisit the Fermi liquid theory using the field-theoretic functional renormalization group formalism and show how the scale invariant fixed point emerges as a local theory, which includes not only the forward scatterings but also non-forward scatterings with small but non-zero momentum transfers. In the low-energy limit, the non-forward scattering amplitude takes a scale invariant form. If the bare coupling is attractive beyond a critical strength, the coupling function exhibits a run-away flow drived by non-forward scattering amplitudes, signifying potential instabilities in particle-hole channels. The pairing interaction also obeys a scaling relation if the center of mass momentum of Cooper pairs is comparable with energy. The coupling functions fully capture the universal low-energy dynamics of the collective modes and instabilities of Fermi liquids. The divergence of the cocupling function in the particle-hole channel beyond a critical interaction suggests an instability toward an ordered phase with a momentum that depends on the interaction strength. At the critical interaction, the instability corresponds to the uniform Pomeranchuk or Stoner instability, but the momentum of the leading instability becomes non-zero for stronger attractive interaction. In the particle-particle channel, the coupling function reveals the dynamics of the unstable mode associated with the BCS instability. When an unstable normal metal evolves into the superconducting state, there exists a period in which a superconducting state with spatially non-uniform phase appears due to the presence of unstable Cooperon modes with non-zero momenta.

cond-mat.str-el↗

arXiv2023

Massless graviton in a model of quantum gravity with emergent spacetime

In the model of quantum gravity proposed in JHEP 2020, 70 (2020), dynamical spacetime arises as a collective phenomenon of underlying quantum matter. Without a preferred decomposition of the Hilbert space, the signature, topology and geometry of an emergent spacetime depend upon how the total Hilbert space is partitioned into local Hilbert spaces. In this paper, it is shown that the massless graviton emerges in the spacetime realized from a Hilbert space decomposition that supports a collection of largely unentangled local clocks.

hep-th↗

arXiv2023

Exact effective action for the O(N) vector model in the large N limit

We present the Wilsonian effective action as a solution of the exact RG equation for the critical $O(N)$ vector model in the large $N$ limit. Below four dimensions, the exact effective action can be expressed in a closed form as a transcendental function of two leading scaling operators with infinitely many derivatives. From the exact solution that describes the RG flow from a UV theory to the fixed point theory in the IR, we obtain the mapping between UV operators and IR scaling operators. It is shown that IR scaling operators are given by sums of infinitely many UV operators with infinitely many derivatives.

hep-th↗

arXiv2023

Field-theoretic functional renormalization group formalism for non-Fermi liquids and its application to the antiferromagnetic quantum critical metal in two dimensions

To capture the universal low-energy physics of metals within effective field theories, one has to generalize the usual notion of scale invariance and renormalizable field theory due to the presence of intrinsic scales (Fermi momenta). In this paper, we develop a field-theoretic functional renormalization group formalism for full low-energy effective field theories of non-Fermi liquids that include all gapless modes around the Fermi surface. The formalism is applied to the non-Fermi liquid that arises at the antiferromagnetic quantum critical point in two space dimensions. In the space of coupling functions, an interacting fixed point arises at a point with momentum-independent couplings and vanishing nesting angle. In theories deformed with non-zero nesting angles, coupling functions acquire universal momentum profiles controlled by the bare nesting angles at low energies before flowing to superconducting states in the low-energy limit. The superconducting instability is unavoidable because lukewarm electrons that are coherent enough to be susceptible to pairing end up being subject to a renormalized attractive interaction with its minimum strength set by the nesting angle. Despite the inevitable superconducting instability, theories with small bare nesting angles and bare four-fermion couplings that are repulsive or weakly attractive must pass through the region with slow RG flow due to the proximity to the non-Fermi liquid fixed point. The bottleneck region controls the scaling behaviours of the normal state and the quasi-universal pathway from the non-Fermi liquid to superconductivity. In the limit that the nesting angle is small, the non-Fermi liquid scaling dictates the physics over a large window of energy scale above the superconducting transition temperature.

cond-mat.str-el↗

arXiv2022

Ultraviolet-Infrared Mixing in Marginal Fermi Liquids

When Fermi surfaces (FSs) are subject to long-range interactions that are marginal in the renormalization-group sense, Landau Fermi liquids are destroyed, but only barely. With the interaction further screened by particle-hole excitations through one-loop quantum corrections, it has been believed that these marginal Fermi liquids (MFLs) are described by weakly coupled field theories at low energies. In this Letter, we point out a possibility in which higher-loop processes qualitatively change the picture through UV-IR mixing, in which the size of the FS enters as a relevant scale. The UV-IR mixing effect enhances the coupling at low energies, such that the basin of attraction for the weakly coupled fixed point of a $(2+1)$-dimensional MFL shrinks to a measure-zero set in the low-energy limit. This UV-IR mixing is caused by gapless virtual Cooper pairs that spread over the entire FS through marginal long-range interactions. Our finding signals a possible breakdown of the patch description for the MFL and questions the validity of using the MFL as the base theory in a controlled scheme for non-Fermi liquids that arise from relevant long-range interactions.

cond-mat.str-el↗

arXiv2021

Constraints on beta functions in field theories

The $β$-functions describe how couplings run under the renormalization group flow in field theories. In general, all couplings that respect the symmetry and locality are generated under the renormalization group flow, and the exact renormalization group flow is characterized by the $β$-functions defined in the infinite dimensional space of couplings. In this paper, we show that the renormalization group flow is highly constrained so that the $β$-functions defined in a measure zero subspace of couplings completely determine the $β$-functions in the entire space of couplings. We provide a quantum renormalization group-based algorithm for reconstructing the full $β$-functions from the $β$-functions defined in the subspace. As examples, we derive the full $β$-functions for the $O(N)$ vector model and the $O_L(N) \times O_R(N)$ matrix model entirely from the $β$-functions defined in the subspace of single-trace couplings.

hep-th↗

arXiv2021

Ultraviolet/infrared mixing in non-Fermi liquids

We study low-energy effective field theories for non-Fermi liquids with Fermi surfaces of general dimensions and co-dimensions. When the dimension of Fermi surface is greater than one, low-energy particle-hole excitations remain strongly coupled with each other across the entire Fermi surface. In this case, even the observables that are local in the momentum space (such as the Green's functions) become dependent on the size of the Fermi surface in singular ways, resulting in an ultraviolet/infrared (UV/IR) mixing. By tuning the dimension and co-dimension of the Fermi surface independently, we find perturbative non-Fermi liquid fixed points controlled by both UV/IR mixing and interactions.

cond-mat.str-el↗

arXiv2021

Clock-dependent spacetime

Einstein's theory of general relativity is based on the premise that the physical laws take the same form in all coordinate systems. However, it still presumes a preferred decomposition of the total kinematic Hilbert space into local kinematic Hilbert spaces. In this paper, we consider a theory of quantum gravity that does not come with a preferred partitioning of the kinematic Hilbert space. It is pointed out that, in such a theory, dimension, signature, topology and geometry of spacetime depend on how a collection of local clocks is chosen within the kinematic Hilbert space.

gr-qc↗

arXiv2020

A model of quantum gravity with emergent spacetime

We construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal flavours, and columns label spatial sites. In the limit that the size of the matrix is large, the sites can collectively form a spatial manifold. The manifold is determined from the pattern of entanglement present across local Hilbert spaces associated with column vectors of the matrix. With no structure of manifold fixed in the background, the spacetime gauge symmetry is generalized to a group that includes diffeomorphism in arbitrary dimensions. The momentum and Hamiltonian that generate the generalized diffeomorphism obey a first-class constraint algebra at the quantum level. In the classical limit, the constraint algebra of the general relativity is reproduced as a special case. The first-class nature of the algebra allows one to express the projection of a quantum state of the matrix to a gauge-invariant state as a path integration of dynamical variables that describe collective fluctuations of the matrix. The collective variables describe dynamics of emergent spacetime, where multi-fingered times arise as Lagrangian multipliers that enforce the gauge constraints. If the quantum state has a local structure of entanglement, a smooth spacetime with well-defined dimension, topology, signature and geometry emerges at the saddle-point, and the spin two mode that determines the geometry can be identified. We find a saddle-point solution that describes a series of (3+1)-dimensional de Sitter-like spacetimes with the Lorentzian signature bridged by Euclidean spaces in between. Fluctuations of the collective variables are described by bi-local fields that propagate in the spacetime set up by the saddle-point solution.

hep-th↗