We study the mechanism how critical end points of first-order valence transitions are controlled by a magnetic field. We show that the critical temperature is suppressed to be a quantum critical point (QCP) by a magnetic field and unexpectedly the QCP exhibits nonmonotonic field dependence in the ground-state phase diagram, giving rise to emergence of metamagnetism even in the intermediate valence-crossover regime. The driving force of the field-induced QCP is clarified to be cooperative phenomena of Zeeman effect and Kondo effect, which create a distinct energy scale from the Kondo temperature. This mechanism explains peculiar magnetic response in CeIrIn5 and metamagnetic transition in YbXCu4 for X=In as well as sharp contrast between X=Ag and Cd.
It is shown that unconventional critical phenomena commonly observed in paramagnetic metals YbRh2Si2, YbRh2(Si0.95Ge0.05)2, and beta-YbAlB4 is naturally explained by the quantum criticality of Yb-valence fluctuations. We construct the mode coupling theory taking account of local correlation effects of f electrons and find that unconventional criticality is caused by the locality of the valence fluctuation mode. We show that measured low-temperature anomalies such as divergence of uniform spin susceptibility $χT^{-ζ)$ with $ζ~0.6$ giving rise to a huge enhancement of the Wilson ratio and the em…
The nature of the quantum valence transition is studied in the one-dimensional periodic Anderson model with Coulomb repulsion between f and conduction electrons by the density-matrix renormalization group method. It is found that the first-order valence transition emerges with the quantum critical point and the crossover from the Kondo to the mixed-valence states is strongly stabilized by quantum fluctuation and electron correlation. It is found that the superconducting correlation is developed in the Kondo regime near the sharp valence increase. The origin of the superconductivity is ascribed…
Electronic structures of the quantum critical superconductor beta-YbAlB4 and its polymorph alpha-YbAlB4 are investigated by using bulk-sensitive hard x-ray photoemission spectroscopy. From the Yb 3d core level spectra, the values of the Yb valence are estimated to be ~2.73 and ~2.75 for alpha- and beta-YbAlB4, respectively, thus providing clear evidence for valence fluctuations. The valence band spectra of these compounds also show Yb2+ peaks at the Fermi level. These observations establish an unambiguous case of a strong mixed valence at quantum criticality for the first time among heavy ferm…
On the basis of the Ward-Pitaevskii identity, the residual resistivity $ρ_{0}$ is shown to exhibit huge enhancement around the quantum critical point of valence transition in Ce-based heavy electron systems. This explains a sharp peak of $ρ_{0}$ observed in CeCu$_2$Ge$_2$ under the pressure at $P\sim$16GPa where the superconducting trasition temperature also exhibit the sharp peak.
The roles of critical valence fluctuations of Ce and Yb are discussed as a key origin of several anomalies observed in Ce- and Yb-based heavy fermion systems. Recent development of the theory has revealed that a magnetic field is an efficient control parameter to induce the critical end point of the first-order valence transition. Metamagnetism and non-Fermi liquid behavior caused by this mechanism are discussed by comparing favorably with CeIrIn5, YbAgCu4, and YbIr2Zn20. The interplay of the magnetic order and valence fluctuations offers a key concept for understanding Ce- and Yb-based system…
Many cerium-based heavy fermion (HF) compounds have pressure-temperature phase diagrams in which a superconducting region extends far from a magnetic quantum critical point. In at least two compounds, CeCu2Si2 and CeCu2Ge2, an enhancement of the superconducting transition temperature was found to coincide with an abrupt valence change, with strong circumstantial evidence for pairing mediated by critical valence, or charge transfer, fluctuations. This pairing mechanism, and the valence instability, is a consequence of a f-c Coulomb repulsion term U_fc in the hamiltonian. While some non-supercon…
Despite almost 40 years of research, the origin of heavy-fermion superconductivity is still strongly debated. Especially, the pressure-induced enhancement of superconductivity in CeCu$_2$Si$_2$ away from the magnetic breakdown is not sufficiently taken into consideration. As recently reported in CeCu$_2$Si$_2$ and several related compounds, optimal superconductivity occurs at the pressure of a valence crossover, which arises from a virtual critical end point at negative temperature $T_{\rm cr}$. In this context, we did a meticulous analysis of a vast set of top-quality high-pressure electrical…
Simultaneous resistivity and a.c.-specific heat measurements have been performed under pressure on single crystalline CeCu2Si2 to over 6 GPa in a hydrostatic helium pressure medium. A series of anomalies were observed around the pressure coinciding with a maximum in the superconducting critical temperature, $T_c^{max}$. These anomalies can be linked with an abrupt change of the Ce valence, and suggest a second quantum critical point at a pressure $P_v \simeq 4.5$ GPa, where critical valence fluctuations provide the superconducting pairing mechanism, as opposed to spin fluctuations at ambient p…
A new universality class of quantum criticality emerging in itinerant electron systems with strong local electron correlations is discussed. The quantum criticality of a Ce- or Yb-valence transition gives us a unified explanation for unconventional criticality commonly observed in heavy fermion metals such as YbRh2Si2 and β-YbAlB4, YbCu5-xAlx, and CeIrIn5. The key origin is due to the locality of the critical valence fluctuation mode emerging near the quantum critical end point of the first-order valence transition, which is caused by strong electron correlations for f electrons. Wider relevan…
Effects of inhomogeneous doping on the high-$T_c$ cuprate superconductors are studied within the framework of the t-J model. Especially, the boundary between two non-superconducting regions with doping rates much higher and lower than the optimal one is examined. It is found that, although there is no superconductivity in the bulk, a superconducting region appears at the boundary because singlet resonating valence bond order and holon condensation occur simultaneously in this region. The critical temperature of the induced superconductivity can be higher than that of the optimally doped sample…
The mechanism of how critical end points of the first-order valence transitions (FOVT) are controlled by a magnetic field is discussed. We demonstrate that the critical temperature is suppressed to be a quantum critical point (QCP) by a magnetic field. This results explain the field dependence of the isostructural FOVT observed in Ce metal and YbInCu_4. Magnetic field scan can lead to reenter in a critical valence fluctuation region. Even in the intermediate-valence materials, the QCP is induced by applying a magnetic field, at which the magnetic susceptibility also diverges. The driving force…
Influence of quantum critical point (QCP) of first-order valence transition (FOVT) on Ce- and Yb-based heavy fermions is discussed as a key origin of anomalies such as non-Fermi liquid, metamagnetism, and unconventional superconductivity. Even in intermediate-valence materials, the QCP of the FOVT is shown to be induced by applying a magnetic field, which creates a new characteristic energy distinct from the Kondo temperature. It is stressed that the key concept is closeness to the QCP of the FOVT by pointing out that the proximity of the QCP explains sharp contrast between X=Ag and X=Cd in Yb…
Quantum criticality has been considered to be specific to crystalline materials such as heavy fermions. Very recently, however, the Tsai-type quasicrystal Au51Al34Yb15 has been reported to show unusual quantum critical behavior. To obtain a deeper understanding of this new material, we have searched for other Tsai-type cluster materials. Here, we report that the metal alloys Au44Ga41Yb15 and Ag47Ga38Yb15 are members of the 1/1 approximant to the Tsai-type quasicrystal and that both possess no localized magnetic moment. We suggest that the Au-Al-Yb system is located near the border of the dival…
The mechanism of emergence of robust quantum criticality in Yb- and Ce-based heavy electron systems under pressure is analyzed theoretically. By constructing a minimal model for quasicrystal Yb15Al34Au51 and its approximant, we show that quantum critical points of the first-order valence transition of Yb appear in the ground-state phase diagram with their critical regimes being overlapped to be unified, giving rise to a wide quantum critical regime. This well explains the robust unconventional criticality observed in Yb15Al34Au51 under pressure. We also discuss broader applicability of this me…
Quantum criticality due to the valence transition in some Yb-based heavy fermion metals has gradually turned out to play a crucial role to understand the non-Fermi liquid properties that cannot be understood from the conventional quantum criticality theory due to magnetic transitions. Namely, critical exponents giving the temperature (T) dependence of the resistivity ρ(T), the Sommerfeld coefficient, C(T)/T, the magnetic susceptibility, χ(T), and the NMR relaxation rates, 1/(T_{1}T), can be understood as the effect of the critical valence fluctuations of f electrons in Yb ion in a unified way.…
Ubiquity of unconventional phenomena observed in a series of heavy fermion metals is discussed on the basis of an idea of critical valence fluctuations. After surveying experimental aspects of these unconventional behaviors in prototypical compounds, CeCu_2(Si,Ge)_2, under pressure, we propose that sharp valence crossover phenomena are realized in CeCu_6, CeRhIn_5, and Ce(Ir,Rh)Si_3 by tuning the pressure and the magnetic field simultaneously, on the basis of previous results for an extended Anderson lattice model with the Coulomb repulsion U_fc between localized f-electron and itinerant condu…
Progress of theories and experiments of the quantum valence criticality is overviewed focusing on recent discoveries of direct evidence of quantum critical point of valence transitions in periodic crystal $α$-YbAl$_{1-x}$Fe$_x$B$_4$ at $x=0.014$ and quasicrystal Yb$_{15}$(Al$_{1-x} $Ga$_{x}$)$_{34}$(Au$_{1-y}$Cu$_{y}$)$_{51}$ at $x=y=0$. The common quantum criticality as well as $T/B$ scaling behavior in the magnetization observed in the periodic crystal $β$-YbAlB$_4$ and quasicrystal Yb$_{15}$Al$_{34}$Au$_{51}$ is shown to be explained from the theory of critical Yb-valence fluctuations start…
We present the pressure-temperature phase diagram of the antiferromagnet CeAg$_2$Si$_2$ established via resistivity and calorimetry measurements under quasi-hydrostatic conditions up to 22.5~GPa. With increasing pressure, the Néel temperature [$T_{\mathrm{N}}(p=0)=8.6$~K] slowly increases up to $T_{\mathrm{N}}=13.4$~K at 9.4~GPa and then vanishes abruptly at the magnetic critical pressure $p_{\mathrm{c}}\sim13$~GPa. For the first time, heavy fermion superconductivity is observed in CeAg$_2$Si$_2$ . Superconductivity emerges at $\sim 11$~GPa and persists over roughly 10~GPa. Partial- and bulk-t…
The mechanism of the emergence of robust quantum criticality in the heavy-electron quasicrystal Yb15Al34Au51 is analyzed theoretically. By constructing a minimal model for the quasicrystal and its crystalline approximant, which contain concentric shell structures with Yb and Al-Au clusters, we show that a set of quantum critical points of the first-order valence transition of Yb appears as spots in the ground-state phase diagram. Their critical regions overlap each other, giving rise to a wide quantum critical region. This well explains the robust criticality observed in Yb15Al34Au51 under pre…
We present a valence bond theory of the spin-S quantum Heisenberg model. For nonfrustracting, local exchange and dimension d > 1, it predicts a resonating ground state with bond amplitudes h(r) ~ (a^2+r^2)^(-p/2) and decay exponent p=d+1. Different values of p can be achieved by introducing frustrating (p > d+1) or nonfrustrating (p < d+1) long-range interactions. For d=2, but not d=3, there is a critical value of the decay exponent p_c above which the ground state is a spin liquid. The phase transition is analogous to quantum percolation, with fractal valence bond loops playing the role of pe…
Fermi liquid theory, the standard theory of metals, has been challenged by a number of observations of anomalous metallic behavior found in the vicinity of a quantum phase transition. The breakdown of the Fermi liquid is accomplished by fine-tuning the material to a quantum critical point using a control parameter such as the magnetic field, pressure, or chemical composition. Our high precision magnetization measurements of the ultrapure f-electron based superconductor β-YbAlB4 demonstrate a scaling of its free energy indicative of zero-field quantum criticality without tuning in a metal. The …
The $S=1/2$ square-lattice $J$-$Q$ model hosts a deconfined quantum phase transition between antiferromagnetic and dimerized (valence-bond solid) ground states. We here study two deformations of this model -- a term projecting staggered singlets as well as a modulation of the $J$ terms forming alternating "staircases" of strong and weak couplings. The first deformation preserves all lattice symmetries. Using quantum Monte Carlo simulations, we show that it nevertheless introduces a second relevant field, likely by producing topological defects. The second deformation induces helical valence-bo…
UTe$_2$ is a recently discovered unconventional superconductor that has attracted much interest due to its many intriguing properties - a large residual density-of-states in the superconducting state, re-entrant superconductivity in high magnetic fields, and potentially spin-triplet topological superconductivity. Our ac calorimetry, electrical resistivity, and x-ray absorption study of UTe$_2$ under applied pressure reveals key new insights on the superconducting and magnetic states surrounding pressure-induced quantum criticality at P$_{c1}$ = 1.3 GPa. First, our specific heat data at low pre…
We study a spin-1/2 SU(2) model on the honeycomb lattice with nearest-neighbor antiferromagnetic exchange $J$ that favors Néel order, and competing 6-spin interactions $Q$ which favor a valence bond solid (VBS) state in which the bond-energies order at the "columnar" wavevector ${\mathbf K} = (2π/3,-2π/3)$. We present quantum Monte-Carlo evidence for a direct continuous quantum phase transition between Néel and VBS states, with exponents and logarithmic violations of scaling consistent with those at analogous deconfined critical points on the square lattice. Although this strongly suggests a d…
Intermetallic compounds containing $f$-electron elements have been prototypical materials for investigating strong electron correlations and quantum criticality (QC). Their heavy fermion ground state evoked by the magnetic $f$-electrons is susceptible to the onset of quantum phases, such as magnetism or superconductivity, due to the enhanced effective mass ($m^{*}$) and a corresponding decrease of the Fermi temperature. However, the presence of $f$-electron valence fluctuations to a non-magnetic state is regarded an anathema to QC, as it usually generates a paramagnetic Fermi-liquid state with…
The magnetic, transport, and thermal properties of single crystals of the series Fe(Ga1-xGex)3 are reported. Pure FeGa3 is a nonmagnetic semiconductor, that when doped with small concentrations of Ge (extrinsic electrons), passes through an insulator-to-metal transition and displays non-Fermi liquid (NFL) behavior. Moreover, we observer clear signatures of a ferromagnetic quantum critical point (FM-QCP) in this system at x = 0.052. The mechanism of the local moment formation is consistent with a one-electron reduction of Fe dimer singlets, a unique structural feature in FeGa3, where the densit…
We report Resonant inelastic x-ray scattering measurements (RIXS) in YbCu$_2$Si$_2$ at the Yb L$_{3}$ edge under high pressure (up to 22 GPa) and at low temperatures (down to 7 K) with emphasis on the vicinity of the transition to a magnetic ordered state. We find a continuous valence change towards the trivalent state with increasing pressure but with a pronounced change of slope close to the critical pressure. Even at 22 GPa the Yb$^{+3}$ state is not fully achieved. The pressure where this feature is observed decreases as the temperature is reduced to 9 GPa at 7K, a value close to the criti…
In the quest for materials with unconventional quantum phases, the organic triangular-lattice antiferromagnet $κ$-(ET)$_2$Cu$_2$(CN)$_3$ has been extensively discussed as a quantum spin liquid (QSL) candidate. Recently, an intriguing quantum critical behaviour was suggested from low-temperature magnetic torque experiments. Through microscopic analysis of all anisotropic contributions, including Dzyaloshinskii-Moriya and multi-spin scalar chiral interactions, we highlight significant deviations of the experimental observations from a quantum critical scenario. Instead, we show that disorder-ind…
Unconventional quantum criticality in heavy-fermion systems has been extensively analyzed in terms of a critical destruction of the Kondo effect. Motivated by a recent demonstration of quantum criticality in a mixed-valent heavy-fermion system, β-YbAlB4, we study a particle-hole-asymmetric Anderson impurity model with a pseudogapped density of states. We demonstrate Kondo destruction at a mixed-valent quantum critical point, where a collapsing Kondo energy scale is accompanied by a singular charge-fluctuation spectrum. Both spin and charge responses scale with energy over temperature (ω/T) and…
We report large-scale quantum Monte Carlo calculations at the T=0 antiferromagnetic to valence-bond-solid (VBS) transition of a two-dimensional S=1/2 XY model with four-spin interactions. Finite-size scaling suggests a discontinuous spin stiffness, but a continuous VBS order-parameter. We propose that this is a continuous VBS transition without critical spin fluctuations. We also argue that the system is close to a point, in an extended parameter space, where both the magnetic and VBS fluctuations are critical--possibly a deconfined quantum-critical point.
We study the impurity physics at a continuous quantum phase transition from an SU(3) symmetric Néel ordered state to a valence bond solid state that breaks lattice symmetries, using quantum Monte Carlo techniques. This continuous transition is expected to be an example of `deconfined criticality' in an SU(3) symmetric system. We find that the spin-texture induced by a missing-spin defect at the transition takes on a finite-size scaling form consistent with expectations from standard scaling arguments at a scale-invariant quantum critical point, albeit with significant subleading power-law fini…
We review the evidence supporting valence-fluctuation mediated superconductivity in CeCu2Si2 and CeCu2Ge2, where Tc reaches 2.4 K at high pressure. In these systems the valence and magnetic critical points, at p_V and p_c respectively, are well separated. Characteristic signatures associated with both phenomena are distinct. In contrast, the valence and spin fluctuation regions appear much closer in most Ce based compounds. Concerning d-transition metals, superconductivity in pure iron emerges in the pressure window 15-30 GPa with the onset of Tc up to almost 3 K. All relevant observations poi…
The scaling behavior over four decades of the ratio of temperature T to magnetic field B observed in the magnetization in beta-YbAlB4 is theoretically examined. By developing a theoretical framework that exhibits the quantum critical phenomena of Yb-valence fluctuations under a magnetic field, we show that the T/B-scaling behavior can appear near the quantum critical point of the valence transition. The emergence of the T/B scaling indicates the presence of the small characteristic energy scale of critical Yb-valence fluctuations. It is argued that the quantum valence criticality offers a unif…
Implementation of the hardcore-dimer Hilbert space in cold Rydberg-atom simulators opens a new route of investigating real-time dynamics of dimer liquids under Hamiltonian quench. Here, we consider an initial Resonating Valence Bond (RVB) state on the square lattice realizing a critical Coulomb phase with algebraic and dipolar correlations. Using its representation as a special point of a broad manifold of SU($2$)-symmetric, translationnally invariant, Projected Entangled Pair States (PEPS), we compute its non-equilibrium dynamics upon turning on inter-site Heisenberg interactions. We show tha…
We report electrical resistivity, ac magnetic susceptibility and X-ray absorption spectroscopy measurements of intermediate valence YbNi$_{3}$Ga$_{9}$ under pressure and magnetic field. We have revealed a characteristic pressure-induced Yb valence crossover within the temperature-pressure phase diagram, and a first-order metamagnetic transition is found below $P_{\rm c}$ $\sim$ 9 GPa where the system undergoes a pressure-induced antiferromagnetic transition. As a possible origin of the metamagnetic behavior, a critical valence fluctuation emerging near the critical point of the first-order val…
We investigate the arguably simplest $SU(2)$-invariant wave functions capable of accounting for spin-liquid behavior, expressed in terms of nearest-neighbor valence-bond states on the square lattice and characterized by different topological invariants. While such wave-functions are known to exhibit short-range spin correlations, we perform Monte Carlo simulations and show that four-point correlations decay algebraically with an exponent $1.16(4)$. This is reminiscent of the {\it classical} dimer problem, albeit with a slower decay. Furthermore, these correlators are found to be spatially modu…
We investigate the valence transition in three-dimensional topological Kondo insulator through slave-boson analysis of periodic Anderson model. By including the effect of intra-atomic Coulomb correlation $U_{fc}$ between conduction and local electrons, we find a first-order valence transition from Kondo region to mixed valence upon ascending of local level above a critical $U_{fc}$, and this valence transition usually occurs very close to or simultaneously with a topological transition. Near the parameter region of zero-temperature valence transition, rise of temperature can generate a thermal…
We uncover new topology-related features of the $π$-flux saddle-point solution of the $D$=2+1 Heisenberg antiferromagnet. We note that symmetries of the spinons sustain a built-in competition between antiferromagnetic (AF) and valence-bond-solid (VBS) orders, the two tendencies central to recent developments on quantum criticality. An effective theory containing an analogue of the Wess-Zumino-Witten term is derived, which generates quantum phases related to AF monopoles with VBS cores, and reproduces Haldane's hedgehog Berry phases. The theory readily generalizes to $π$-flux states for all $D$…
We present numerical evidence for the emergence of an extended valence bond solid (VBS) phase at $T=0$ in the kagome $S=1/2$ Heisenberg antiferromagnet with ferromagnetic further-neighbor interactions. The VBS is located at the boundary between two magnetically ordered regions and extends close to the nearest-neighbor Heisenberg point. It exhibits a diamond-like singlet covering pattern with a $12$-site unit-cell. Our results suggest the possibility of a direct, possibly continuous, quantum phase transition from the neighboring $\mathbf{q}=0$ coplanar magnetically ordered phase into the VBS ph…
The effect of pressure on the unique electronic state of the antiferromagnetic (AF) compound EuCu2Ge2 has been measured in a wide temperature range from 10 mK to 300 K by electrical resistivity measurements up to 10 GPa. The Neel temperature of TN = 15 K at ambient pressure increases monotonically with increasing pressure and becomes a maximum of TN = 27 K at 6.2 GPa but suddenly drops to zero at Pc = 6.5 GPa, suggesting the quantum critical point (QCP) of the valence transition of Eu from a nearly divalent state to that with trivalent weight. The rhomag0 and A values obtained from the low-tem…
We discuss how Anderson's ideas of nominal and real valence can be incorporated into the current discussion of heavy electron quantum criticality. In the heavy electron phase, the nominal valence of a screened magnetic ion differs from its real valence by one unit. We identify this discrepancy with the formation of a positively charged background we call the Kondo pseudo-potential. At the quantum critical point, the sudden collapse of the heavy electron Fermi surface can be identified with the return of the nominal to the real valence. This leads to the interesting idea that the heavy electron…
We consider spin-half quantum antiferromagnets in two spatial dimensions in the quantum limit, where the spins are in a valence bond solid (VBS) phase. The transitions between two such VBS phases is studied. In some cases, an interesting second order transition controlled by a fixed line with varying critical exponents if found. A specific example is provided by an antiferromagnetically coupled bilayer system on the honeycomb lattice where a continuous quantum phase transition can generically exist between two VBS phases. Furthermore, these critical points are deconfined, in the sense that gap…
It was reported by Shiino et al in J. Phys. Soc. Jpn. 86, 123705 (2017) that Ce_xLa_{1-x} Cu_{5.62} Au_{0.38} (x=0.02-0.10) exhibits a new type of quantum criticality in both magnetic and thermal properties, which is the same as that observed in a series of materials exhibiting quantum critical valence fluctuations (QCVF), such as β-YbAlB_4, Yb_{15}Al_{34}Au_{51}, and so on. However, the temperature (T) dependence in the resistivity rho(T) for T<0.5K is quite anomalous, i.e., ρ(T)\propto (const.-T^{n}) with n \simeq 0.75 at x=0.05. We find that this anomalous exponent is given by n=2(1-ζ), wit…
We use quantum Monte Carlo simulations to study a quantum $S=1/2$ spin model with competing multi-spin interactions. We find a quantum phase transition between a columnar valence-bond solid (cVBS) and a Néel antiferromagnet (AFM), as in the scenario of deconfined quantum-critical points, as well as a transition between the AFM and a staggered valence-bond solid (sVBS). By continuously varying a parameter, the sVBS--AFM and AFM--cVBS boundaries merge into a direct sVBS--cVBS transition. Unlike previous models with putative deconfined AFM--cVBS transitions, e.g., the standard $J$-$Q$ model, in o…
We show theoretically that the nuclear spin-lattice relaxation rate (T_1T)^{-1} and the spin susceptibility exhibit divergent behaviors toward zero temperature at the quantum critical point (QCP) of the first-order valence transition. Remarkable enhancement in (T_1T)^{-1} and the spin susceptibility is induced by valence fluctuations even at the valence-crossover temperature far away from the QCP. This mechanism well explains peculiar behaviors observed recently in YbAuCu_4 and also gives a systematic explanation for YbXCu_4 for X=In, Au, Ag, Tl, and Pd from the viewpoint of the closeness to t…
We study the finite temperature properties of quantum magnets close to a continuous quantum phase transition between two distinct valence bond solid phases in two spatial dimension. Previous work has shown that such a second order quantum `Lifshitz' transition is described by a free field theory and is hence tractable, but is nevertheless non-trivial. At $T>0$, we show that while correlation functions of certain operators exhibit $ω/T$ scaling, they do not show analogous scaling in space. In particular, in the scaling limit, all such correlators are purely {\em local} in space, although the sa…
Here we provide the first clear evidence of Fermi-liquid breakdown in an intermediate valence system. We employ high precision magnetization measurements of the valence fluctuating superconductor beta-YbAlB4 to probe the quantum critical free energy down to temperatures far below the characteristic energy scale of the valence fluctuations. The observed T/B scaling in the magnetization over three decades not only indicates unconventional quantum criticality, but places an upper bound on the critical magnetic field |B_c| < 0.2 mT, a value comparable with the Earth's magnetic field and six orders…
Various samples of sodium cobalt oxyhydrate with relatively large amounts of Na$^{+}$ ions were synthesized by a modified soft-chemical process in which a NaOH aqueous solution was added in the final step of the procedure. From these samples, a superconducting phase diagram was determined for a section of a cobalt valence of $\sim$+3.48, which was compared with a previously obtained one of $\sim$+3.40. The superconductivity was significantly affected by the isovalent exchanger of Na$^{+}$ and H$_{3}$O$^{+}$, rather than by variation of Co valence, suggesting the presence of multiple kinds of F…
Quantum dimer models exhibit quantum critical points and liquid states when the ground state is the resonating-valence bond (RVB) state. We construct SU(2)-invariant spin-1/2 Hamiltonians with the same RVB ground state. The main technical obstacle overcome is the fact that different "dimer" configurations in the spin model are not orthogonal to each other. We show that the physics depends on how dimers are related to the spins, and find a Hamiltonian that may be quantum critical.
We study the S=1/2 Heisenberg (J) model on the two-dimensional square lattice in the presence of additional higher-order spin interactions (Q) which lead to a valence-bond-solid (VBS) ground state. Using quantum Monte Carlo simulations, we analyze the thermal VBS transition. We find continuously varying exponents, with the correlation-length exponent "nu" close to the Ising value for large Q/J and diverging when Q/J approaches the quantum-critical point (the critical temperature Tc -> 0). This is in accord with the theory of deconfined quantum-critical points, which predicts that the transitio…
Using ground-state projector quantum Monte Carlo simulations in the valence bond basis, it is demonstrated that non-frustrating four-spin interactions can destroy the Neel order of the two-dimensional S=1/2 Heisenberg antiferromagnet and drive it into a valence-bond solid (VBS) phase. Results for spin and dimer correlations are consistent with a single continuous transition, and all data exhibit finite-size scaling with a single set of exponents; z=1, nu=0.78 +/- 0.03, and eta=0.26 +/- 0.03. The unusually large eta and an emergent U(1) symmetry, detected using VBS order parameter histograms, p…
Employing the elemental sensitivity of x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD), we study the valence and magnetic order in the heavy fermion superconductor CeCoIn$_5$. We probe spin population of the f-electrons in Ce and d-electrons in Co as a function of temperature (down to 0.1 K) and magnetic field (up to 6 T). From the XAS we find a pronounced contribution of Ce$^{4+}$ component at low temperature and a clear temperature dependence of the Ce valence below 5 K, suggesting enhanced valence fluctuations, an indication for the presence of a nearby quan…
We investigate the behavior of the periodic Anderson model in the presence of $d$-$f$ Coulomb interaction ($U_{df}$) using mean-field theory, variational calculation, and exact diagonalization of finite chains. The variational approach based on the Gutzwiller trial wave function gives a critical value of $U_{df}$ and two quantum critical points (QCPs), where the valence susceptibility diverges. We derive the critical exponent for the valence susceptibility and investigate how the position of the QCP depends on the other parameters of the Hamiltonian. For larger values of $U_{df}$, the Kondo re…
The breakdown of the lattice Kondo effect in local-moment metals can lead to non-trivial forms of quantum criticality and a variety of non-Fermi-liquid phases. Given indications that Kondo-breakdown transitions involve criticality not only in the spin but also in the charge sector, we investigate the interplay of Kondo breakdown and strong valence fluctuations in generalized Anderson lattice models. We employ a parton mean-field theory to describe the transitions between deconfined fractionalized Fermi liquids and various confined phases. We find that rapid valence changes near Kondo breakdown…
Elucidating the phase diagram of lattice gauge theories with fermionic matter in 2+1 dimensions has become a problem of considerable interest in recent years, motivated by physical problems ranging from chiral symmetry breaking in high-energy physics to fractionalized phases of strongly correlated materials in condensed matter physics. For a sufficiently large number $N_f$ of flavors of four-component Dirac fermions, recent sign-problem-free quantum Monte Carlo studies of lattice quantum electrodynamics (QED$_3$) on the square lattice have found evidence for a continuous quantum phase transiti…
