Phase transitions and symmetry are intimately linked. Melting of ice, for example, restores translation invariance. The mysterious hidden order (HO) phase of URu$_2$Si$_2$ has, despite relentless research efforts, kept its symmetry breaking element intangible. Here we present a high-resolution x-ray diffraction study of the URu$_2$Si$_2$ crystal structure as a function of hydrostatic pressure. Below a critical pressure threshold $p_c\approx3$ kbar, no tetragonal lattice symmetry breaking is observed even below the HO transition $T_{HO}=17.5$ K. For $p>p_c$, however, a pressure-induced rotational symmetry breaking is identified with an onset temperatures $T_{OR}\sim 100$ K. The emergence of an orthorhombic phase is found and discussed in terms of an electronic nematic order that appears unrelated to the HO, but with possible relevance for the pressure-induced antiferromagnetic (AF) phase. Existing theories describe the HO and AF phases through an adiabatic continuity of a complex order parameter. Since none of these theories predicts a pressure-induced nematic order, our finding adds an additional symmetry breaking element to this long-standing problem.
A second-order phase transition is characterized by spontaneous symmetry breaking. The nature of the broken symmetry in the so-called "hidden order" phase transition in the heavy fermion compound URu2Si2, at transition temperature T_h=17.5 K, has posed a long-standing mystery. We report the emergence of an in-plane anisotropy of the magnetic susceptibility below T_h, which breaks the four-fold rotational symmetry of the tetragonal URu2Si2. Two-fold oscillations in the magnetic torque under in-plane field rotation were sensitively detected in small pure crystals. Our findings suggest that the h…
The hidden order in URu$_2$Si$_2$ remains a compelling mystery after more than thirty years, with the order parameter still unidentified. One intriguing proposal for the phase has been hastatic order: a symmetry breaking heavy Fermi liquid with a spinorial hybridization that breaks both single and double time-reversal symmetry. Hastatic order is the first spinorial, rather than vectorial order in materials, but previous work has not yet found direct consequences of the spinorial nature. In this paper, we revisit the hastatic proposal within Landau-Ginzburg theory. Rather than a single spinoria…
Since the 1985 discovery of the phase transition at $T_{\rm HO}=17.5$ K in the heavy-fermion metal URu$_2$Si$_2$, neither symmetry change in the crystal structure nor magnetic ordering have been observed, which makes this "hidden order" enigmatic. Some high-field experiments have suggested electronic nematicity which breaks fourfold rotational symmetry, but direct evidence has been lacking for its ground state at zero magnetic field. Here we report on the observation of lattice symmetry breaking from the fourfold tetragonal to twofold orthorhombic structure by high-resolution synchrotron X-ray…
Despite more than a quarter century of research, the nature of the second-order phase transition in the heavy-fermion metal URu$_2$Si$_2$ remains enigmatic. The key question is which symmetry is being broken below this "hidden order" transition. We review the recent progress on this issue, particularly focusing on the thermodynamic evidence from very sensitive micro-cantilever magnetic torque measurements that the fourfold rotational symmetry of the underlying tetragonal crystal is broken. The angle dependence of the torque under in-plane field rotation exhibits the twofold oscillation term, w…
The heavy-fermion compound URu2Si2 exhibits a hidden-order phase below the temperature, ~ 17.5 K. In spite of intense research for past three decades, no consensus on the order parameter exists and the nature has posed a long-standing mystery. Here we report the discovery of a Griffiths phase within the hidden-order phase, characterized by residual short-range correlations on the collapse of long-range orders due to the dilution effects. In the Griffiths phase scenario, strong evidence are provided for those cluster-like spins, such as the unique power-law behavior of magnetic susceptibility a…
Spontaneous, collective ordering of electronic degrees of freedom leads to second-order phase transitions that are characterized by an order parameter. The notion "hidden order" (HO) has recently been used for a variety of materials where a clear phase transition occurs to a phase without a known order parameter. The prototype example is the heavy-fermion compound URu2Si2 where a mysterious HO transition occurs at 17.5K. For more than twenty years this system has been studied theoretically and experimentally without a firm grasp of the underlying physics. Using state-of-the-art density-functio…
The Fermi surface (FS) nesting properties of URu$_2$Si$_2$ are analyzed with particular focus on their implication for the mysterious hidden order phase. We show that there exist two Fermi surfaces that exhibit a strong nesting at the antiferromagnetic wavevector, $\boldsymbol{Q}_0$=(0,\,0,\,1). The corresponding energy dispersions fulfill the relation $ε_{1}(\boldsymbol{k})$=$- ε_{2} (\boldsymbol{k}\pm \boldsymbol{Q}_0)$ at eight FS hotspot lines. The spin-orbital characters of the involved $5f$ states are {\it distinct} ($j_z$=$\pm$5/2 {\it vs.} $\pm$3/2) and hence the degenerate Dirac cross…
We discuss possible approaches to the problem of the URu2Si2 "Hidden Order" (HO) which remains unsolved after tremendous efforts of researches. Suppose there is no spatial symmetry breaking at the HO transition temperature and solely the time-reversal symmetry breaking emerges owing to some sort of magnetic order. As a result of its 4/mmm symmetry, each uranium atom is a three-dimensional magnetic vortex; its intra-atomic magnetization M(r) is intrinsically non-collinear, so that its dipole, quadrupole and toroidal moments vanish, thus making the vortex "hidden". The first non-zero magnetic mu…
We propose an explanation for the experiment by Schemm et al., Phys. Rev. B 91, 140506 (2015) where the polar Kerr effect (PKE), indicating time-reversal symmetry (TRS) breaking, was observed in the hidden-order (HO) phase of URu2Si2. The PKE signal on warmup was seen only if a training magnetic field was present on cool-down. Using a Ginzburg-Landau model for a complex order parameter, we show that the system can have a metastable ferromagnetic state producing the PKE, even if the HO ground state respects TRS. We predict that a strong reversed magnetic field should reset the PKE to zero.
The conventional order parameters in quantum matters are often characterized by 'spontaneous' broken symmetries. However, sometimes the broken symmetries may blend with the invariant symmetries to lead to mysterious emergent phases. The heavy fermion metal URu2Si2 is one such example, where the order parameter responsible for a second-order phase transition at Th = 17.5 K has remained a long-standing mystery. Here we propose via ab-initio calculation and effective model that a novel spin-orbit density wave in the f-states is responsible for the hidden-order phase in URu2Si2. The staggered spin…
We report a comprehensive electronic structure investigation of the paramagnetic (PM), the large moment antiferromagnetic (LMAF), and the hidden order (HO) phases of URu$_2$Si$_2$. We have performed relativistic full-potential calculations on the basis of the density functional theory (DFT), employing different exchange-correlation functionals to treat electron correlations within the open $5f$-shell of uranium. Specifically, we investigate---through a comparison between calculated and low-temperature experimental properties---whether the $5f$ electrons are localized or delocalized in URu$_2$S…
The development of collective long-range order via phase transitions occurs by the spontaneous breaking of fundamental symmetries. Magnetism is a consequence of broken time-reversal symmetry while superfluidity results from broken gauge invariance. The broken symmetry that develops below 17.5K in the heavy fermion compound URu2Si2 has long eluded such identification. Here we show that the recent observation of Ising quasiparticles in URu2Si2 results from a spinor order parameter that breaks double time-reversal symmetry, mixing states of integer and half-integer spin. Such "hastatic order" hyb…
We studied the uniaxial-pressure dependence of the resistivity for URu$_{2-x}$Fe$_x$Si$_2$ samples with $x$ = 0 and 0.2, which host a hidden order (HO) and a large-moment antiferromagnetic (LMAFM) phase, respectively. For both samples, the elastoresistivity $ζ$ shows a seemingly divergent behavior above the transition temperature $T_0$ and a quick decrease below it. We found that the temperature dependence of $ζ$ for both samples can be well described by assuming the uniaxial pressure effect on the gap or certain energy scale except for $ζ_{(110)}$ of the $x$ = 0 sample, which exhibits a non-z…
Throughout the past three decades the hidden order (HO) problem in URu$_2$Si$_2$ has remained a "hot topic" in the physics of strongly correlated electron systems with well over 600 publications related to this subject. Presently in 2014 there has been significant progress in combining various experimental results embedded within electronic structure calculations using density functional theory (DFT) to give a consistent description of the itinerant behaviour of the HO transition and its low temperature state. Here we review six different experiments: ARPES, quantum oscillations, neutron scatt…
The observation of Ising quasiparticles is a signatory feature of the hidden order phase of URu$_2$Si$_2$. In this paper we discuss its nature and the strong constraints it places on current theories of the hidden order. In the hastatic theory such anisotropic quasiparticles are naturally described described by resonant scattering between half-integer spin conduction electrons and integer-spin Ising moments. The hybridization that mixes states of different Kramers parity is spinorial; its role as an symmetry-breaking order parameter is consistent with optical and tunnelling probes that indicat…
A second-order phase transition is associated with emergence of an "order parameter" and a spontaneous symmetry breaking. For the heavy fermion superconductor URu$_2$Si$_2$, the symmetry of the order parameter associated with its ordered phase below 17.5 K has remained ambiguous despite 30 years of research, and hence is called "hidden order" (HO). Here we use polarization resolved Raman spectroscopy to specify the symmetry of the low energy excitations above and below the HO transition. These excitations involve transitions between interacting heavy uranium 5f orbitals, responsible for the br…
Despite several decades of both experimental and theoretical work the nature of the hidden order transition at THO = 17.5 K in URu2Si2 remains enigmatic. We report here low field DC magnetization as well as AC susceptibility measurements performed on single crystals with field along the c-axis. A peak in the first order AC susceptibility is observed at T=16 K in close proximity to the well known change in slope at THO=17.5 K. Third order susceptibility measurements on the other hand reveal a signature only at 16 K with no discernible change at THO. However, both transitions are visible in the …
We develop a phenomenological mean field theory describing the hidden order phase in URu$_{\text2}$Si$_{\text2}$ as a nematic of the $\text B_{\text{1g}}$ representation staggered along the $c$-axis. Several experimental features are reproduced by this theory: the topology of the temperature--pressure phase diagram, the response of the elastic modulus $(C_{11}-C_{12})/2$ above the transition at ambient pressure, and orthorhombic symmetry breaking in the high-pressure antiferromagnetic phase. In this scenario, hidden order is characterized by broken rotational symmetry that is modulated along t…
A broken symmetry ground state without any magnetic moments has been calculated by means of local-density-approximation to density functional theory plus a local exchange term, the so-called LDA+$U$ approach, for URu$_{2}$Si$_{2}$. The solution is analysed in terms of a multipole tensor expansion of the itinerant density matrix and is found to be a non-trivial magnetic multipole. Analysis and further calculations show that this type of multipole enters naturally in time reversal breaking in presence of large effective spin-orbit coupling and co-exists with magnetic moments for most magnetic ac…
We report the first observation of cyclotron resonance in the hidden-order phase of ultra-clean URu$_2$Si$_2$ crystals, which allows the full determination of angle-dependent electron-mass structure of the main Fermi-surface sheets. We find an anomalous splitting of the sharpest resonance line under in-plane magnetic-field rotation. This is most naturally explained by the domain formation, which breaks the fourfold rotational symmetry of the underlying tetragonal lattice. The results reveal the emergence of an in-plane mass anisotropy with hot spots along the [110] direction, which can account…
This Topical Review describes the multitude of unconventional behaviors in the hidden order, heavy fermion, antiferromagnetic and superconducting phases of the intermetallic compound URu$_2$Si$_2$ when tuned with pressure, magnetic field, and substitutions for all three elements. Such `perturbations' result in a variety of new phases beyond the mysterious hidden order that are only now being slowly understood through a series of state-of-the-science experimentation, along with an array of novel theoretical approaches. Despite all these efforts spanning more than 30 years, hidden order (HO) rem…
Novel electronic states resulting from entangled spin and orbital degrees of freedom are hallmarks of strongly correlated f-electron systems. A spectacular example is the so-called 'hidden-order' phase transition in the heavy-electron metal URu2Si2, which is characterized by the huge amount of entropy lost at T_{HO}=17.5K. However, no evidence of magnetic/structural phase transition has been found below T_{HO} so far. The origin of the hidden-order phase transition has been a long-standing mystery in condensed matter physics. Here, based on a first-principles theoretical approach, we examine t…
In matter, any spontaneous symmetry breaking induces a phase transition characterized by an order parameter, such as the magnetization vector in ferromagnets, or a macroscopic many-electron wave-function in superconductors. Phase transitions with unknown order parameter are rare but extremely appealing, as they may lead to novel physics. An emblematic, and still unsolved, example is the transition of the heavy fermion compound URu$_2$Si$_2$ (URS) into the so-called hidden-order (HO) phase when the temperature drops below $T_0 = 17.5$K. Here we show that the interaction between the heavy fermio…
The hidden order (HO) in URu2Si2 has been determined as a high rank multipole formed by itinerant 5f-electrons with distinct orbital structure imposed by the crystalline electric field. Because this can lead to a considerable number of different multipoles it is of great importance to use microscopic techniques that are sensitive to their subtle physical differences. Here we investigate whether quasiparticle interference (QPI) method can distinguish between the two most frequently proposed HO parameter models: the even rank-4 hexadecapole and the odd-rank-5 dotriacontapole model. We obtain the…
To resolve the nature of the hidden order below 17.5\,K in the heavy fermion compound URu$_2$Si$_2$, identifying which symmetries are broken below the hidden order transition is one of the most important steps. Several recent experiments on the electronic structure have shown that the Fermi surface in the hidden order phase is quite close to the result of band-structure calculations within the framework of itinerant electron picture assuming the antiferromagnetism. This provides strong evidence for the band folding along the c-axis with the ordering vector of $(0\,0\,1)$, corresponding to brok…
d- and f-shells support a large number of local degrees of freedom: dipoles, quadrupoles, octupoles, hexadecapoles, etc. Usually, the ordering of any multipole component leaves the system sufficiently symmetrical to allow a second symmetry breaking transition. Assuming that a second continuous phase transition occurs, we classify the possibilities. We construct the symmetry group of the first ordered phase, and then re-classify the order parameters in the new symmetry. While this is straightforward for dipole or quadrupole order, it is less familiar for octupole order. We give a group theoreti…
We report a comprehensive investigation of the lattice dynamics of URu$_2$Si$_2$ as a function of temperature using Raman scattering, optical conductivity and inelastic neutron scattering measurements as well as theoretical {\it ab initio} calculations. The main effects on the optical phonon modes are related to Kondo physics. The B$_{1g}$ ($Γ_3$ symmetry) phonon mode slightly softens below $\sim$100~K, in connection with the previously reported softening of the elastic constant, $C_{11}-C_{12}$, of the same symmetry, both observations suggesting a B$_{1g}$ symmetry-breaking instability in the…
A systematic search for possible order parameters of the so-called hidden order of URu$_{2}$Si$_{2}$ is conducted. Among the possible candidates that do fulfill the experimental symmetry restrictions on the hidden order parameter, we find one candidate that stand out -- one of the components of a triakontadipole multipole tensor that belongs to the $A_{1u}$ irreducible representation of the point group $D_{4h}$. This solution is characterized by a $\vec{Q}=(0,0,1)$ ordering of the triakontadipoles and has a symmetry that forbids magnetic moments as well as most other multipole ordering on the …
The Fermi liquid approach is applied to the problem of spontaneous violation of the four-fold rotational point-group symmetry ($C_4$) in strongly correlated two-dimensional electronic systems on a square lattice. The symmetry breaking is traced to the existence of a topological phase transition. This continuous transition is triggered when the Fermi line, driven by the quasiparticle interactions, reaches the van Hove saddle points, where the group velocity vanishes and the density of states becomes singular. An unconventional Fermi liquid emerges beyond the implicated quantum critical point.
Motivated by recent observations of $C_4$ symmetry breaking in strongly correlated two-dimensional electron systems on a square lattice, we analyze this phenomenon within an extended Fermi liquid approach. It is found that the symmetry violation is triggered by a continuous topological phase transition associated with exchange of antiferromagnetic fluctuations. In contrast to predictions of mean-field theory, the structure of a part of the single-particle spectrum violating $C_4$ symmetry is found to be highly anisotropic, with a peak located in the vicinity of saddle points.
The observation of cyclotron resonance in ultra-clean crystals of URu2Si2 [S. Tonegawa et al., PRL 109, 036401 (2012)] provides another route besides quantum oscillations to the determination of the bulk electronic structure in the hidden order phase. We report detailed analyses of the resonance lines, which fully resolve the cyclotron mass structure of the main Fermi surface sheets. A particular focus is given to the anomalous splitting of the sharpest resonance line near the [110] direction under in-plane magnetic-field rotation, which implies peculiar electronic structure in the hidden orde…
Novel magnetic phases are expected to occur in highly frustrated spin systems. Here we study the structurally perfect kagomé antiferromagnet CdCu$_3$(OH)$_6$(NO$_3$)$_2\cdot$H$_2$O by magnetization, magnetic torque, and heat capacity measurements using single crystals.An antiferromagnetic order accompanied by a small spontaneous magnetization that surprisingly is confined in the kagomé plane sets in at $T_\mathrm{N}\approx$4 K, well below the nearest-neighbor exchange interaction $J / k_B$ = 45 K.This suggests that a unique $\bf q = 0$ type 120$^\circ$ spin structure with "negative" (downward)…
For reasonable parameters a hole bound to a Na^{+} acceptor in Ca_{2-x}Na_{x}CuO_{2}Cl_{2} has a doubly degenerate ground state whose components can be represented as states with even (odd) reflection symmetry around the x(y) -axes. The conductance pattern for one state is anisotropic as the tip of a tunneling microscope scans above the Cu-O-Cu bonds along the x(y)-axes. This anisotropy is pronounced at lower voltages but is reduced at higher voltages. Qualitative agreement with recent experiments leads us to propose this effect as an explanation of the broken local rotational symmetry.
Adding a second Kondo channel to heavy fermion materials reveals new exotic symmetry breaking phases associated with the development of Kondo coherence. In this paper, we review two such phases, the "hastatic order" associated with non-Kramers doublet ground states, where the two-channel nature of the Kondo coupling is guaranteed by virtual valence fluctuations to an excited Kramers doublet, and "composite pair superconductivity," where the two channels differ by charge 2e and can be thought of as virtual valence fluctuations to a pseudo-isospin doublet. The similarities and differences betwee…
In the triangular layered magnet PdCrO2 the intralayer magnetic interactions are strong, however the lattice structure frustrates interlayer interactions. In spite of this, long-range, 120$^\circ$ antiferromagnetic order condenses at $T_N = 38$~K. We show here through neutron scattering measurements under in-plane uniaxial stress and in-plane magnetic field that this occurs through a spontaneous lifting of the three-fold rotational symmetry of the nonmagnetic lattice, which relieves the interlayer frustration. We also show through resistivity measurements that uniaxial stress can suppress ther…
The magnetic and nematic properties of the iron chalcogenides have recently been the subject of intense interest. Motivated by the proposed antiferroquadrupolar and Ising-nematic orders for the bulk FeSe, we study the phase diagram of an $S=1$ generalized bilinear-biquadratic model with multi-neighbor interactions. We find a large parameter regime for a ($π$,0) antiferroquadrupolar phase, showing how quantum fluctuations stabilize it by lifting an infinite degeneracy of certain semiclassical states. Evidence for this C$_4$-symmetry-breaking quadrupolar phase is also provided by an unbiased den…
We introduce a matrix product state (MPS) with an incommensurate periodicity by applying the spin-rotation operator of each site to a uniform MPS in the thermodynamic limit. The spin rotations decrease the variational energy with accompanying translational symmetry breaking and the rotational symmetry breaking in the spin space even if the Hamiltonian has the both symmetries. The optimized pitch of rotational operator reflects the commensurate/incommensurate properties of spin-spin correlation functions in the $S=1/2$ Heisenberg chain and the $S=1/2$ ferro-antiferro zigzag chain.
We investigate the physical consequences of orbital current patterns (OCP) in doped two-leg Cu-O Hubbard ladders. The internal symmetry of the pattern, in the case of the ladder structure, differs slightly from that suggested so far for cuprates. We focus on this OCP and look for measurable signatures of its existence. We compute the magnetic field produced by the OCP at each lattice site, and estimate its value in view of a possible experimental detection. Using a renormalization group (RG) analysis, we determine the changes that are caused by the SU(2) spin-rotational symmetry breaking which…
We analyze multi-orbital Hubbard models describing Hund's metals, focusing on the ubiquitous occurrence of a charge instability, signalled by a divergent/negative electronic compressibility, in a range of doping from the half-filled Mott insulator corresponding to the frontier between Hund's and normal metals. We show that the breaking of rotational invariance favors this instability: both spin-anisotropy in the interaction and crystal-field splitting among the orbitals make the instability zone extend to larger dopings, making it relevant for real materials like iron-based superconductors. Th…
Revealing Rotational Symmetry Breaking Charge-density Wave Order in Kagome Superconductor (Rb, K)V$_3$Sb$_5$ by Ultrafast Pump-probe Experiments
University of Pennsylvania（宾夕法尼亚大学）；Weizmann Institute of Science（魏茨曼科学研究所）；University of California Santa Barbara（加州大学圣巴巴拉分校）；Oak Ridge National Laboratory（橡树岭国家实验室）
We investigate Cu-doped Ba(Fe$_{1-x}$Cu$_x$)$_2$As$_2$ with transport, magnetic susceptibility, and elastic neutron scattering measurements. In the heavily Cu-doped regime where long-range stripe-type antiferromagnetic order in BaFe$_2$As$_2$ is suppressed, Ba(Fe$_{1-x}$Cu$_x$)$_2$As$_2$ (0.145 $\leq x \leq$ 0.553) samples exhibit spin-glass-like behavior in magnetic susceptibility and insulating-like temperature dependence in electrical transport. Using elastic neutron scattering, we find stripe-type short-range magnetic order in the spin-glass region identified by susceptibility measurements…
It is suggested that marked features of symmetry breaking mechanism and elementary excitations in chiral helimagnet come up as visible effects in electron spin resonance (ESR) profile. Under the magnetic field applied parallel and perpendicular to the helical axis, elementary excitations are respectively described by the helimagnon associated with rotational symmetry breaking and the magnetic kink crystal phonon associated with translational symmetry breaking. We demonstrate how the ESR spectra distinguish these excitations.
The interplay between dimensionality and various phases of matter is a central inquiry in condensed matter physics. New phases are often discovered through spontaneously broken symmetry. Understanding the dimensionality of superconductivity in the high-temperature cuprate analogue $-$ layered nickelates and revealing a new symmetry-breaking state are the keys to deciphering the underlying pairing mechanism. Here, we demonstrate the highly-tunable dimensionality and a broken rotational symmetry state in the superconductivity of square-planar layered nickelates. The superconducting state, probed…
Kondo insulator samarium hexaboride (SmB6) has been intensely studied in recent years as a potential candidate of a strongly correlated topological insulator. One of the most exciting phenomena observed in SmB6 is the clear quantum oscillations appearing in magnetic torque at a low temperature despite the insulating behavior in resistance. These quantum oscillations show multiple frequencies and varied effective masses. The origin of quantum oscillation is, however, still under debate with evidence of both two-dimensional Fermi surfaces and three-dimensional Fermi surfaces. Here, we carry out …
Motivated by recent reports of nematic order in twisted bilayer graphene (TBG), we investigate the impact of the triangular moiré superlattice degrees of freedom on nematicity. In TBG, the nematic order parameter is not Ising-like, as it is the case in tetragonal crystals, but has a 3-state Potts character related to the threefold rotational symmetry ($C_{3z}$) of the moiré superlattice. We find that even in the presence of static strain that explicitly breaks the $C_{3z}$ symmetry, the system can still undergo a nematic-flop phase transition that spontaneously breaks in-plane twofold rotation…
Nematic phase transitions in high-temperature superconductors have a strong impact on the electronic properties of these systems. BaFe$_2$As$_2$,\@ with an established nematic transition around 137 K induced by magnetic fluctuations, and BaNi$_2$As$_2$,\@ a non-magnetic analog of BaFe$_2$As$_2$ with a structural transition in the same temperature range,\@ share a common tetragonal aristotype crystal structure with space-group type $I4/mmm$.\@ In contrast to BaFe$_2$As$_2$ where collinear stripe magnetic order is found for the orthorhombic low-$T$ phase, a unidirectional charge density wave tog…
Broken fourfold rotational (C$_4$) symmetry is observed in the experimental properties of several classes of unconventional superconductors. It has been proposed that this symmetry breaking is important for superconducting pairing in these materials, but in the high superconducting transition temperature (high-T$_{\mathrm{c}}$) cuprates this broken symmetry has never been observed on the Fermi surface. We have measured a pronounced anisotropy in the angle dependence of the interlayer magnetoresistance of the underdoped high-T$_{\mathrm{c}}$) superconductor YBa$_2$Cu$_3$O$_{6.58}$, directly rev…
We introduce a family of spin-1/2 quantum chains, and show that their exact ground states break the rotational and translational symmetries of the original Hamiltonian. We also show how one can use projection to construct a spin-3/2 quantum chain with nearest neighbor interaction, whose exact ground states break the rotational symmetry of the Hamiltonian. Correlation functions of both models are determined in closed form. Although we confine ourselves to examples, the method can easily be adapted to encompass more general models.
Tower of States analysis is a powerful tool for investigating phase transitions in condensed matter systems. Spontaneous symmetry breaking implies a specific structure of the energy eigenvalues and their corresponding quantum numbers on finite systems. In these lecture notes we explain the group representation theory used to derive the spectral structure for several scenarios of symmetry breaking. We give numerous examples to compute quantum numbers of the degenerate groundstates, including translational symmetry breaking or spin rotational symmetry breaking in Heisenberg antiferromagnets. The…
We show that singlet superconductivity in the Abrikosov vortex phase is absolutely unstable with respect to the appearance of a chiral triplet component of a superconducting order parameter. This chiral component, p_x + i p_y, breaks time-reversal, parity, and spin rotational symmetries of the internal order parameter, responsible for a relative motion of two electrons in the Cooper pair. We demonstrate that the symmetry breaking Pauli paramagnetic effects can be tuned by a magnetic field strength and direction and can be made of the order of unity in organic and high-temperature layered super…
